monetary incentives in italian public administration: a ......strong enough to make the initial...
TRANSCRIPT
Research ArticleMonetary Incentives in Italian Public Administration AStimulus for Employees An Agent-Based Approach
Linda Ponta 1 Gian Carlo Cainarca 2 and Silvano Cincotti 2
1LIUC-Cattaneo University Corso G Matteotti 23 I-21053 Castellanza VA Italy2DIME-DOGE University of Genoa Via Opera Pia 15 I-16145 Genova Italy
Correspondence should be addressed to Silvano Cincotti silvanocincottiunigeit
Received 7 February 2020 Accepted 22 April 2020 Published 23 May 2020
Academic Editor Dehua Shen
Copyright copy 2020 Linda Ponta et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
e paper focusing on the context of Public Administration (PA) addresses the effects of monetary incentives in employeesrsquoperformance In the Italian PA the monetary incentives are distributed according to the DL15009 (ie the monetary incentivesare divided among the employees according to the employeesrsquo performance) which is based on the rank order tournament epaper investigates if this mechanism has positive and sustainable impacts on the employeesrsquo performance in the short middle andlong terme employeesrsquo performance has beenmodeled as a function of ability andmotivatione results of the computationalexperiments show a positive impact of the monetary incentives distributed according to merit criteria on the employeesrsquoperformance in the short middle and long term
1 Introduction
Starting from the late 1970s many European countries haveexperienced a period of reforms in the public sector ereforms regarded different fields and in particular from oneside the management system introducing control andplanning system and from the other the performance ap-praisal and the reward systems fostering technical andcultural changes in the public sector [1ndash8] In Italy since theearly 1990s numerous reforms have been succeeded with thepurpose of reaching a better use of the resources and a betterquality of services given to citizen It is worth noting thatreforms in Italy are characterized by a ldquotop-downrdquo approachie by regulation and the most important are D Lgs 291993 and Law n 5997 (so called Legge Bassanini) esereforms tried to adopt new managerial instruments usuallyused in the private sector but the results were a failurebecause the transferability of these instruments to the bu-reaucracy of the Public Administration (PA) is not alwayseffective e main causes of the failure were the constraintsof PA such as the possibility to make change only by meansof laws and the uncertainty of the amount of resources elast attempt of reform is the ldquoDecreto Legislativo 27 ottobre
2009 n 150rdquo ldquoAttuazione della legge 4 marzo 2009 n 15 inmateria di ottimizzazione della produttivita del lavoropubblico e di efficienza e trasparenza delle pubblicheamministrazioni (09G0164)rdquo also called Brunetta reformwhere a virtuous circle able to induce behaviors more ef-ficient to overcome the previous failure is initiated givinginstruments extremely concrete and ready to use Followingthe New Public Management theory (NPM) the Brunettareform considers the PA as firms and borrows from the firmcontext the key concepts of efficiency efficacy productivityand transparency In particular the efficiency connects theresources used (input) with the results (output) thetransparency means the possibility of the citizen to access tothe activity of PA the efficacy considers the measure of theaction of the PA on the external environment and finally theproductivity means the performance of the employees and ofthe organization In fact according to NPM performancemanagement based on objectives monitoring and incen-tives must be introduced in public sector organizations [6]Focusing on the incentives and in particular on the mon-etary incentives given to the employees according to DL15009 the incentives are nomore divided equally among theemployees but they are distributed only to the employees
HindawiComplexityVolume 2020 Article ID 6152017 13 pageshttpsdoiorg10115520206152017
that perform better ranking them according to merit cri-teria In fact as stated in [9 10] pay-for-performancesystems are less efficient than the promotion tournaments inpublic organizations
e main goal of the paper is to verify the effects of thenew incentives mechanism introduced with DL15009 inthe Italian PA and to observe its sustainability over time Inorder to address such investigation the paper presents anagent-based model and simulation based on empirical datacollected by questionnaires Simulation is a useful tool toinvestigate complex systems in many different fields such asengineering physics mathematics and economics and isalso becoming an increasingly significant methodologicalapproach in organizations and strategy and public man-agement field [11ndash16] Among the different simulationmodels the agent-based approach is very useful to inves-tigate complex systems and networks characterized by alarge number of simple interacting units [17ndash26] An agent-based model provides a computational laboratory verysuitable to make classical what-if analysis by means of ex-periments [27ndash33] In organizations field agent-basedmodels (ABMs) are particularly well suited to study pro-cesses where heterogenous interacting entities are involved[34ndash37] us they represent a useful tool to investigate theeffects of new policies such as new incentive mechanisms Inthe following Section 2 presents the literary review and theresearch gap Section 3 the questionnaire data Section 4 thesimulation model Section 5 the computational experimentsand Section 6 the empirical analysis Finally Section 7provides the discussion and conclusions of the study
2 Literature Review and Research Question
In the literature many studies about the increasing of ef-ficiency and performance of the PA have been presented[38] Usually the organizational performance is considereddirectly related to the performance of employees and how toevaluate the performance of employees in the public sector isan interesting and difficult field of research [39ndash42] emain theories consider jointly the ldquocapacity to workrdquo and theldquowill to workrdquo to determine the employeesrsquo performance[43 44] e ldquocapacity to workrdquo has been formalized asability whereas the ldquowill to workrdquo as motivation [45] Someyears later to improve the effective evaluation of the em-ployeesrsquo contribution the Ability Motivation and Oppor-tunity model (AMOmodel) which adds the ldquoopportunity toperformrdquo to the ldquocapacity to workrdquo and ldquowill to workrdquo hasbeen defined [46 47] According to this theory HumanResearch (HR) system is viewed as a composition of em-ployee skills motivation and opportunity to contribute inworking life [46 48ndash52]
21 Monetary Reward It is already known that the eco-nomic motivation is one of the most used stimuli to improvethe firm performance [53 54] Focusing on the relationbetween monetary incentives and employeesrsquo performanceone of the most important theories is Performance RelatedPay (PRP) theory derived from the principles of Weberian
bureaucracy see [55] for further details With respect to asystem that grants a bonus based on seniority PRP is amechanism able to quickly increase work motivation andimprove the performance of employees [56] in fact em-ployees work harder if they valuing the monetary rewardstrust that those awards are related to their increased efforts[57 58]
In the literature the use of financial incentives and inparticular of monetary incentives is based primarily on thetheoretical propositions of reinforcement theory [59] andexpectancy theory [60] Reinforcement theory premised onthe principles and techniques aimed at modifying organi-zational behavior investigates the connection between thetarget behavior (eg performance) and the motivational tool(eg pay for performance) [61ndash63] whereas expectancytheory is an analytical tool to study how a reward systemmotivates the employees [64]
Other theories useful to investigate the link betweenincentives and motivation are the equity theory and thedistributive justice According to the equity theory eachemployee compares herhis contribution to the organizationwith the reward gained by herhis job [65] and with the oneobtained by other coworkers Instead the idea of distributivejustice is connected to the one of procedural justiceAccording to procedural justice individuals evaluate themechanism that the organization introduces to distributerewards [66]
Several studies in the literature state that the efficacy ofmonetary incentives is connected to specific conditions oforganizations In particular they argue that individualeconomic incentives are not so useful in the traditionalpublic sector if the medical and educational contexts areexcluded [54 59 67ndash71]
In particular a study focused on public managers reportsthat financial rewards had no significant effect on themanagersrsquo effort [72] It is worth noting that the relationshipbetween incentive and performance in public and privatesector has different peculiarities mainly due to specificity ofcultural dimension market relations bonus size andnonexpandable business constraints [67 73] Finally in thePA the link between incentive and performance is notstraightforward because it is difficult to identify the con-tribution of each employee In fact in private firms this iseasier because the results of operations are quantitativelymeasurable whereas in the public sector where profit is notthe primary target this is more difficult us an evaluationschemes designed to capture the different levels of com-petence and predisposition of individuals to make a greatereffort in the workplace can be adopted
22 Research Gap In this paper the employeesrsquo perfor-mance is evaluated focusing on their abilities and motiva-tions Manymechanisms can be used to detect the abilities ofemployees [74] but all of them can be attributed to twofundamental models the subjective evaluations that con-sider the individual organizational behavior and the ob-jective evaluations that directly take into account thefeedback of one or more superior or all of the colleagues
2 Complexity
Focusing on the objective evaluation the network analysismainly focused on the links among the employees allows toevaluate the importance and relevance of each employeewith respect to herhis colleagues Indeed the relationshipsin the informal network reflect the recognition given to asingle employee from their colleagues for herhis skills andherhis opportunities to participate in working life
e ability is also a measure of employees to makethemselves available by their colleagues [75 76]
e motivation is reflected considering a model withdifferent levels of stimuli that depend on the employeesrsquostrength and successes ey are represented by theachievement of a predetermined threshold that leads todifferent monetary rewards [77] is model is based on theexpectancy theory of motivation a process theory that pro-vides an explanation of individual criteria used to chooseamong different behaviors According to this theory the workmotivation depends on the perceived association betweenperformance and outcomes Employeesmodify their behaviorbased on their estimation of anticipated outcomes [78]According to [79] the motivation for work is related to aseries of causes and effects first of all persons should trust thattheir increased efforts will translate into a better performancesecondary a satisfactory performance should lead to a wantedreward thirdly the reward should fulfill a significant need forthe individual Finally the desire to fulfill this need should bestrong enough to make the initial efforts worthwhile
So far in the PA the financial incentives are distributedamong the employees following a hierarchical mechanismwithout considering the performance of each employeeSpecifically the incentives are first uniformly distributedamong the business units and then subdivided among in-dividual employees e portion of incentives received byeach employee is proportional to its tenure ie related to therole in the organization not determined by its performance
As mentioned in the introduction the Italian DL15009tried to introduce a merit logic in the distribution ofmonetary incentives in the PA According to the DL15009the bonus is evaluated with a merit logic which is formalizedby the closed rank tournament theory which means that theemployees are ranked and only a subset takes the monetaryincentives according to the employeesrsquo performanceAccording to this law the employees are divided in three setscalled set A B and C and receive a different amount ofmonetary incentives according to the set In particular 25of the total employees is collocated in set A 50 in set B and25 in set C e total amount of monetary incentives isdivided as follows 50 to set A 50 to set B and 0 to setC us people in set C do not receive any kind of monetaryincentives
e main research question of the paper is to investigateif the monetary incentives distributed according to meritcriteria ie according to DL 15009 are a stimulus forbetter performance in the short middle and long term eeffect of the introduction of DL15009 is investigatedconsidering the sustainability of the new rules for the dis-tribution of incentives along time using the agent-basedsimulation e simulation verifies if the monetary incen-tives distributed with merit criteria have positive or negative
effect after the introduction of the rule In detail the sus-tainability of the merit criteria in the distribution of mon-etary incentives is investigated considering how manyemployees every year are in the same set and how manyemployees change set trying to improve their performance
3 The Data
A series of interviews has been arranged in order to explorethe connection between the performance of the employeesand the allocation of economic incentives in February 2011131 employees were interviewed and in January 2013 thearranged interviews were 126 e interviews consisted ofone hour face-to-face sessions composed of 57 questions towhich the employees had to respond with a value between 1and 7 according to the Likert scale [80] e employeesinterviewed belong to five different organizational areas Inorder to minimize misunderstandings the research teamdirectly administered the questionnaires e questionnaireswere anonymous the provided data were only used forprivate purposes and the people were interviewed inagreement with the trade unions In February 2011 126questionnaires were collected out of 131 (four employeeswere absent in that period and one was hired as a temporarysecretary) In 2013 interviewees were 123 out of a total of126 e total number of employees decreased because therehave been a few retirements and due to the financial crisisthe assumption rate was lower than the retirement rate equestionnaires were composed of four different sections
(i) Personal data (gender and age)(ii) Position (tenure and organizational area)(iii) Skills (problem solving teamwork determination
customer oriented and self-organization)(iv) Intraorganization relationship
e resultant set of data provides information on bothemployee characteristics (occupied position knowledgeskills and background) and the organizational model (therelationships maintained between employees of the sameorganization and between different organizations) In ad-dition to this data the HR department provided the salaryinformation of employees for the three years from 2010 to2012 Specifically this information included
(i) e uniformly distributed portion of the bonusgranted to every employee
(ii) e portion of the bonus based on the criteria ofmerit
(iii) e salary-level there are 12 levels 8 of which arereserved for employees having nonexecutivepositions
It is worth noting that in 2010 the total amount ofincentives distributed equally among the business units was47 and the one distributed according the merit criteria was53 whereas in 2011 the allocation was 36 and 64respectively us the monetary incentives distributedaccording the merit criteria increases from 53 to 64
Complexity 3
4 The Model
41 e Network e employees in the model are orga-nized as a directed graph where the employees are thenodes and the arrows represent the interactions amongemployees e total number of employees is N and eachemployee is characterized by an identification number idAn employee is linked to a set of other employees whosenumber and strength (of the connection) gij depends onthe real data e connections among the employees havebeen determined ignoring the vertical relation amongsupervisors and employees and considering the informalnetwork created by means of the information obtainedwith the administered questionnaire In fact employeeswere asked with whom and how many times they need tointeract to perform the given task In particular they hadto indicate up to ten members of the organization theyneed to relate more directly and more frequently with inorder to improve or facilitate the execution of their ac-tivities In order to quantify the frequency of the con-nection ie the strength a Likert scale that ranges from 1(contacts infrequent some once a month) to 7 (severaltimes per day) has been used With the collected infor-mation an adjacency squared and not symmetricalmatrix has been built and shown in the informal networkof Figure 1 It is worth remarking that only the con-nections between employees in the same level have beenconsidered to find out only the ldquohorizontalrdquorelationships
e interactions in the graph are assumed to be uni-directional (ie if employee j influences employee i it doesnot necessarily mean that employee i influences employee j)and characterized by a weight gji assumed a positive realnumber in the range [0 1] proportional to the Likert scaleAs a directed graph is used both an output and input nodedegrees are defined e output node degree is associated tothe output branches of a given node whereas the input nodedegree is related to the input arrows
Furthermore each employee is characterized by herhisrank r and herhis performance P
At each time step h the performance of employee i isevaluated and the rank rh
i is updatede agentrsquos rank r is aninteger number between 1 and 3 depending on the set towhich the employee belongs Employees in set A have rankrh
i 1 in set B have rank rhi 2 and in set C have rank
rhi 3 According to their performance in descending orderthe employees are divided in three set A B and C Set A isformed by the top 25 of the total employees set B by thenext 50 and set C by the last 25 (see DL 15009 formore details) It is worth remembering that employeesbelonging to different sets receive a different fraction ofmonetary incentives In particular half of the total amountof monetary incentives is divided among employees in set Ahalf among employees in set B and 0 among employees inset C
e graph is responsible for the changes in employeesrsquorank In fact at each time step employees depending ontheir rank change a fraction of hisher connections in orderto improve the performance
42 e Performance As already stated in Section 2 theperformance is a function of Ability and Motivationsand quantitatively the performance is measured asthe production of ability and motivation [43] Informulas
Performance Ability times Motivation (1)
421 Ability As already stated in Section 2 in order todetect the abilities of employees the objective evaluationshave been considered by using the network analysis ap-proach Generally speaking the influence of an individualregarding other individuals within a network is indicated byhisher centrality [81]
Centrality in the advice network means the recognitiongiven to a single employee from herhis colleagues for theavailability in exchanging advices and in problem solving Acentral individual can increase knowledge about differentproblems over the years and as more and more colleaguesbecome dependent on herhim for some help shehe gainspower and authority [82 83] ere are many definitions ofcentrality but the most common are the Degree theCloseness the Betweenness the Coreness and the Bonacichcentrality [84ndash87]
In this paper among the others the degree centrality ischosen and the centrality is measured by means of thenumber of connections among the employees defining thecentrality index
e centrality index of employee i CIi indicates therelationship between employee i and the other employeesand in particular quantifies how employee i is involved inthe activities of the other employees
CIi TACi
cmax (2)
where TACi is the task advice centrality of employee i andcmax is the maximum number of input connections amongall the employees e task advice centrality for each nodeie the centrality of the individual in the social consultingnetwork is the sum of all incoming arrows (input nodedegree) multiplied by their weights As mentioned abovethe employeersquos centrality in the intraorganizational net-work reflects herhis skills to participate in working lifeand in particular indicates how a node is necessary toperform the employeesrsquo activities us it is a proxy of theemployeesrsquo ability In the formula the task advice cen-trality of employee i (TACi) is
TACi 1113944j
cjigji (3)
where cji are the incoming arrows of employee i and gji arethe respective weights
422 Motivation As stated in Section 2 the expectancytheory of motivation has been considered According to thistheory employees can be motivated if they believe that thereis a positive correlation between efforts and performanceis behavior has been schematized defining the motivation
4 Complexity
index MI In particular the motivation of employee i isquantified with the motivation index MIi According to DL15009 the employees are ranked and divided in three sets AB and C and receive a different fraction of monetary in-centive In particular 25 of the total employees is collo-cated in set A 50 in set B and 25 in set C respectivelywhereas half of the total amount of monetary incentives isdivided among employees in set A half among employees inset B and 0 among employees in set Cemotivation indexquantifies the motivation of each employee to do better inorder to receive more monetary incentive According to thedeprivation-satiation proposition the more often in therecent past a person has received a major award the less hewill confer a value to any further reward Following thisproposition for employees in set A (corresponding to highincentives) the motivation decreases increasing the per-formance evaluation and conversely for employees in set Cthe motivation increases if performance evaluation in-creases In particular the employees near the upper bound ofset A and the lower bound of set C are not motivated to dobetter [88] In the formula the motivation index MIA in setA is
MIA Es minus P
11138681113868111386811138681113868111386811138681113868
Es minus Ta( 1113857 (4)
where Es is the maximum value of performance in set A Ta
the minimum value of performance in set A P is the em-ployee performance and the motivation index in set C andMIC is
MIC P minus Ei
11138681113868111386811138681113868111386811138681113868
Tb minus Ei( 1113857 (5)
where Ei is the minimum value of rank in set C and Tb themaximum value of rank in set C For employees in set B themotivation is high when the employee is near the twobounds of the range and decreases in the middle is is inline with the theory that while choosing among differentactions an employee chooses the one for which the resultsmultiplied by the probability of getting it is greater [88]
MIB Tmb minus P
11138681113868111386811138681113868111386811138681113868
Ta minus Tb( 11138572 (6)
where Tmb is the middle value of rank in set B Table 1summarizes the parameters abbreviations
Figure 2 shows how the motivation index MI rangesalong the set A B and C
Employees in set A increase their motivation movingtheir level of assessment from Es (maximum level of as-sessment) to Ta Employees in set C decrease their moti-vation moving their level of assessment from Tb to Ei
Figure 1 Network of employees at time t 0
Complexity 5
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
that perform better ranking them according to merit cri-teria In fact as stated in [9 10] pay-for-performancesystems are less efficient than the promotion tournaments inpublic organizations
e main goal of the paper is to verify the effects of thenew incentives mechanism introduced with DL15009 inthe Italian PA and to observe its sustainability over time Inorder to address such investigation the paper presents anagent-based model and simulation based on empirical datacollected by questionnaires Simulation is a useful tool toinvestigate complex systems in many different fields such asengineering physics mathematics and economics and isalso becoming an increasingly significant methodologicalapproach in organizations and strategy and public man-agement field [11ndash16] Among the different simulationmodels the agent-based approach is very useful to inves-tigate complex systems and networks characterized by alarge number of simple interacting units [17ndash26] An agent-based model provides a computational laboratory verysuitable to make classical what-if analysis by means of ex-periments [27ndash33] In organizations field agent-basedmodels (ABMs) are particularly well suited to study pro-cesses where heterogenous interacting entities are involved[34ndash37] us they represent a useful tool to investigate theeffects of new policies such as new incentive mechanisms Inthe following Section 2 presents the literary review and theresearch gap Section 3 the questionnaire data Section 4 thesimulation model Section 5 the computational experimentsand Section 6 the empirical analysis Finally Section 7provides the discussion and conclusions of the study
2 Literature Review and Research Question
In the literature many studies about the increasing of ef-ficiency and performance of the PA have been presented[38] Usually the organizational performance is considereddirectly related to the performance of employees and how toevaluate the performance of employees in the public sector isan interesting and difficult field of research [39ndash42] emain theories consider jointly the ldquocapacity to workrdquo and theldquowill to workrdquo to determine the employeesrsquo performance[43 44] e ldquocapacity to workrdquo has been formalized asability whereas the ldquowill to workrdquo as motivation [45] Someyears later to improve the effective evaluation of the em-ployeesrsquo contribution the Ability Motivation and Oppor-tunity model (AMOmodel) which adds the ldquoopportunity toperformrdquo to the ldquocapacity to workrdquo and ldquowill to workrdquo hasbeen defined [46 47] According to this theory HumanResearch (HR) system is viewed as a composition of em-ployee skills motivation and opportunity to contribute inworking life [46 48ndash52]
21 Monetary Reward It is already known that the eco-nomic motivation is one of the most used stimuli to improvethe firm performance [53 54] Focusing on the relationbetween monetary incentives and employeesrsquo performanceone of the most important theories is Performance RelatedPay (PRP) theory derived from the principles of Weberian
bureaucracy see [55] for further details With respect to asystem that grants a bonus based on seniority PRP is amechanism able to quickly increase work motivation andimprove the performance of employees [56] in fact em-ployees work harder if they valuing the monetary rewardstrust that those awards are related to their increased efforts[57 58]
In the literature the use of financial incentives and inparticular of monetary incentives is based primarily on thetheoretical propositions of reinforcement theory [59] andexpectancy theory [60] Reinforcement theory premised onthe principles and techniques aimed at modifying organi-zational behavior investigates the connection between thetarget behavior (eg performance) and the motivational tool(eg pay for performance) [61ndash63] whereas expectancytheory is an analytical tool to study how a reward systemmotivates the employees [64]
Other theories useful to investigate the link betweenincentives and motivation are the equity theory and thedistributive justice According to the equity theory eachemployee compares herhis contribution to the organizationwith the reward gained by herhis job [65] and with the oneobtained by other coworkers Instead the idea of distributivejustice is connected to the one of procedural justiceAccording to procedural justice individuals evaluate themechanism that the organization introduces to distributerewards [66]
Several studies in the literature state that the efficacy ofmonetary incentives is connected to specific conditions oforganizations In particular they argue that individualeconomic incentives are not so useful in the traditionalpublic sector if the medical and educational contexts areexcluded [54 59 67ndash71]
In particular a study focused on public managers reportsthat financial rewards had no significant effect on themanagersrsquo effort [72] It is worth noting that the relationshipbetween incentive and performance in public and privatesector has different peculiarities mainly due to specificity ofcultural dimension market relations bonus size andnonexpandable business constraints [67 73] Finally in thePA the link between incentive and performance is notstraightforward because it is difficult to identify the con-tribution of each employee In fact in private firms this iseasier because the results of operations are quantitativelymeasurable whereas in the public sector where profit is notthe primary target this is more difficult us an evaluationschemes designed to capture the different levels of com-petence and predisposition of individuals to make a greatereffort in the workplace can be adopted
22 Research Gap In this paper the employeesrsquo perfor-mance is evaluated focusing on their abilities and motiva-tions Manymechanisms can be used to detect the abilities ofemployees [74] but all of them can be attributed to twofundamental models the subjective evaluations that con-sider the individual organizational behavior and the ob-jective evaluations that directly take into account thefeedback of one or more superior or all of the colleagues
2 Complexity
Focusing on the objective evaluation the network analysismainly focused on the links among the employees allows toevaluate the importance and relevance of each employeewith respect to herhis colleagues Indeed the relationshipsin the informal network reflect the recognition given to asingle employee from their colleagues for herhis skills andherhis opportunities to participate in working life
e ability is also a measure of employees to makethemselves available by their colleagues [75 76]
e motivation is reflected considering a model withdifferent levels of stimuli that depend on the employeesrsquostrength and successes ey are represented by theachievement of a predetermined threshold that leads todifferent monetary rewards [77] is model is based on theexpectancy theory of motivation a process theory that pro-vides an explanation of individual criteria used to chooseamong different behaviors According to this theory the workmotivation depends on the perceived association betweenperformance and outcomes Employeesmodify their behaviorbased on their estimation of anticipated outcomes [78]According to [79] the motivation for work is related to aseries of causes and effects first of all persons should trust thattheir increased efforts will translate into a better performancesecondary a satisfactory performance should lead to a wantedreward thirdly the reward should fulfill a significant need forthe individual Finally the desire to fulfill this need should bestrong enough to make the initial efforts worthwhile
So far in the PA the financial incentives are distributedamong the employees following a hierarchical mechanismwithout considering the performance of each employeeSpecifically the incentives are first uniformly distributedamong the business units and then subdivided among in-dividual employees e portion of incentives received byeach employee is proportional to its tenure ie related to therole in the organization not determined by its performance
As mentioned in the introduction the Italian DL15009tried to introduce a merit logic in the distribution ofmonetary incentives in the PA According to the DL15009the bonus is evaluated with a merit logic which is formalizedby the closed rank tournament theory which means that theemployees are ranked and only a subset takes the monetaryincentives according to the employeesrsquo performanceAccording to this law the employees are divided in three setscalled set A B and C and receive a different amount ofmonetary incentives according to the set In particular 25of the total employees is collocated in set A 50 in set B and25 in set C e total amount of monetary incentives isdivided as follows 50 to set A 50 to set B and 0 to setC us people in set C do not receive any kind of monetaryincentives
e main research question of the paper is to investigateif the monetary incentives distributed according to meritcriteria ie according to DL 15009 are a stimulus forbetter performance in the short middle and long term eeffect of the introduction of DL15009 is investigatedconsidering the sustainability of the new rules for the dis-tribution of incentives along time using the agent-basedsimulation e simulation verifies if the monetary incen-tives distributed with merit criteria have positive or negative
effect after the introduction of the rule In detail the sus-tainability of the merit criteria in the distribution of mon-etary incentives is investigated considering how manyemployees every year are in the same set and how manyemployees change set trying to improve their performance
3 The Data
A series of interviews has been arranged in order to explorethe connection between the performance of the employeesand the allocation of economic incentives in February 2011131 employees were interviewed and in January 2013 thearranged interviews were 126 e interviews consisted ofone hour face-to-face sessions composed of 57 questions towhich the employees had to respond with a value between 1and 7 according to the Likert scale [80] e employeesinterviewed belong to five different organizational areas Inorder to minimize misunderstandings the research teamdirectly administered the questionnaires e questionnaireswere anonymous the provided data were only used forprivate purposes and the people were interviewed inagreement with the trade unions In February 2011 126questionnaires were collected out of 131 (four employeeswere absent in that period and one was hired as a temporarysecretary) In 2013 interviewees were 123 out of a total of126 e total number of employees decreased because therehave been a few retirements and due to the financial crisisthe assumption rate was lower than the retirement rate equestionnaires were composed of four different sections
(i) Personal data (gender and age)(ii) Position (tenure and organizational area)(iii) Skills (problem solving teamwork determination
customer oriented and self-organization)(iv) Intraorganization relationship
e resultant set of data provides information on bothemployee characteristics (occupied position knowledgeskills and background) and the organizational model (therelationships maintained between employees of the sameorganization and between different organizations) In ad-dition to this data the HR department provided the salaryinformation of employees for the three years from 2010 to2012 Specifically this information included
(i) e uniformly distributed portion of the bonusgranted to every employee
(ii) e portion of the bonus based on the criteria ofmerit
(iii) e salary-level there are 12 levels 8 of which arereserved for employees having nonexecutivepositions
It is worth noting that in 2010 the total amount ofincentives distributed equally among the business units was47 and the one distributed according the merit criteria was53 whereas in 2011 the allocation was 36 and 64respectively us the monetary incentives distributedaccording the merit criteria increases from 53 to 64
Complexity 3
4 The Model
41 e Network e employees in the model are orga-nized as a directed graph where the employees are thenodes and the arrows represent the interactions amongemployees e total number of employees is N and eachemployee is characterized by an identification number idAn employee is linked to a set of other employees whosenumber and strength (of the connection) gij depends onthe real data e connections among the employees havebeen determined ignoring the vertical relation amongsupervisors and employees and considering the informalnetwork created by means of the information obtainedwith the administered questionnaire In fact employeeswere asked with whom and how many times they need tointeract to perform the given task In particular they hadto indicate up to ten members of the organization theyneed to relate more directly and more frequently with inorder to improve or facilitate the execution of their ac-tivities In order to quantify the frequency of the con-nection ie the strength a Likert scale that ranges from 1(contacts infrequent some once a month) to 7 (severaltimes per day) has been used With the collected infor-mation an adjacency squared and not symmetricalmatrix has been built and shown in the informal networkof Figure 1 It is worth remarking that only the con-nections between employees in the same level have beenconsidered to find out only the ldquohorizontalrdquorelationships
e interactions in the graph are assumed to be uni-directional (ie if employee j influences employee i it doesnot necessarily mean that employee i influences employee j)and characterized by a weight gji assumed a positive realnumber in the range [0 1] proportional to the Likert scaleAs a directed graph is used both an output and input nodedegrees are defined e output node degree is associated tothe output branches of a given node whereas the input nodedegree is related to the input arrows
Furthermore each employee is characterized by herhisrank r and herhis performance P
At each time step h the performance of employee i isevaluated and the rank rh
i is updatede agentrsquos rank r is aninteger number between 1 and 3 depending on the set towhich the employee belongs Employees in set A have rankrh
i 1 in set B have rank rhi 2 and in set C have rank
rhi 3 According to their performance in descending orderthe employees are divided in three set A B and C Set A isformed by the top 25 of the total employees set B by thenext 50 and set C by the last 25 (see DL 15009 formore details) It is worth remembering that employeesbelonging to different sets receive a different fraction ofmonetary incentives In particular half of the total amountof monetary incentives is divided among employees in set Ahalf among employees in set B and 0 among employees inset C
e graph is responsible for the changes in employeesrsquorank In fact at each time step employees depending ontheir rank change a fraction of hisher connections in orderto improve the performance
42 e Performance As already stated in Section 2 theperformance is a function of Ability and Motivationsand quantitatively the performance is measured asthe production of ability and motivation [43] Informulas
Performance Ability times Motivation (1)
421 Ability As already stated in Section 2 in order todetect the abilities of employees the objective evaluationshave been considered by using the network analysis ap-proach Generally speaking the influence of an individualregarding other individuals within a network is indicated byhisher centrality [81]
Centrality in the advice network means the recognitiongiven to a single employee from herhis colleagues for theavailability in exchanging advices and in problem solving Acentral individual can increase knowledge about differentproblems over the years and as more and more colleaguesbecome dependent on herhim for some help shehe gainspower and authority [82 83] ere are many definitions ofcentrality but the most common are the Degree theCloseness the Betweenness the Coreness and the Bonacichcentrality [84ndash87]
In this paper among the others the degree centrality ischosen and the centrality is measured by means of thenumber of connections among the employees defining thecentrality index
e centrality index of employee i CIi indicates therelationship between employee i and the other employeesand in particular quantifies how employee i is involved inthe activities of the other employees
CIi TACi
cmax (2)
where TACi is the task advice centrality of employee i andcmax is the maximum number of input connections amongall the employees e task advice centrality for each nodeie the centrality of the individual in the social consultingnetwork is the sum of all incoming arrows (input nodedegree) multiplied by their weights As mentioned abovethe employeersquos centrality in the intraorganizational net-work reflects herhis skills to participate in working lifeand in particular indicates how a node is necessary toperform the employeesrsquo activities us it is a proxy of theemployeesrsquo ability In the formula the task advice cen-trality of employee i (TACi) is
TACi 1113944j
cjigji (3)
where cji are the incoming arrows of employee i and gji arethe respective weights
422 Motivation As stated in Section 2 the expectancytheory of motivation has been considered According to thistheory employees can be motivated if they believe that thereis a positive correlation between efforts and performanceis behavior has been schematized defining the motivation
4 Complexity
index MI In particular the motivation of employee i isquantified with the motivation index MIi According to DL15009 the employees are ranked and divided in three sets AB and C and receive a different fraction of monetary in-centive In particular 25 of the total employees is collo-cated in set A 50 in set B and 25 in set C respectivelywhereas half of the total amount of monetary incentives isdivided among employees in set A half among employees inset B and 0 among employees in set Cemotivation indexquantifies the motivation of each employee to do better inorder to receive more monetary incentive According to thedeprivation-satiation proposition the more often in therecent past a person has received a major award the less hewill confer a value to any further reward Following thisproposition for employees in set A (corresponding to highincentives) the motivation decreases increasing the per-formance evaluation and conversely for employees in set Cthe motivation increases if performance evaluation in-creases In particular the employees near the upper bound ofset A and the lower bound of set C are not motivated to dobetter [88] In the formula the motivation index MIA in setA is
MIA Es minus P
11138681113868111386811138681113868111386811138681113868
Es minus Ta( 1113857 (4)
where Es is the maximum value of performance in set A Ta
the minimum value of performance in set A P is the em-ployee performance and the motivation index in set C andMIC is
MIC P minus Ei
11138681113868111386811138681113868111386811138681113868
Tb minus Ei( 1113857 (5)
where Ei is the minimum value of rank in set C and Tb themaximum value of rank in set C For employees in set B themotivation is high when the employee is near the twobounds of the range and decreases in the middle is is inline with the theory that while choosing among differentactions an employee chooses the one for which the resultsmultiplied by the probability of getting it is greater [88]
MIB Tmb minus P
11138681113868111386811138681113868111386811138681113868
Ta minus Tb( 11138572 (6)
where Tmb is the middle value of rank in set B Table 1summarizes the parameters abbreviations
Figure 2 shows how the motivation index MI rangesalong the set A B and C
Employees in set A increase their motivation movingtheir level of assessment from Es (maximum level of as-sessment) to Ta Employees in set C decrease their moti-vation moving their level of assessment from Tb to Ei
Figure 1 Network of employees at time t 0
Complexity 5
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
Focusing on the objective evaluation the network analysismainly focused on the links among the employees allows toevaluate the importance and relevance of each employeewith respect to herhis colleagues Indeed the relationshipsin the informal network reflect the recognition given to asingle employee from their colleagues for herhis skills andherhis opportunities to participate in working life
e ability is also a measure of employees to makethemselves available by their colleagues [75 76]
e motivation is reflected considering a model withdifferent levels of stimuli that depend on the employeesrsquostrength and successes ey are represented by theachievement of a predetermined threshold that leads todifferent monetary rewards [77] is model is based on theexpectancy theory of motivation a process theory that pro-vides an explanation of individual criteria used to chooseamong different behaviors According to this theory the workmotivation depends on the perceived association betweenperformance and outcomes Employeesmodify their behaviorbased on their estimation of anticipated outcomes [78]According to [79] the motivation for work is related to aseries of causes and effects first of all persons should trust thattheir increased efforts will translate into a better performancesecondary a satisfactory performance should lead to a wantedreward thirdly the reward should fulfill a significant need forthe individual Finally the desire to fulfill this need should bestrong enough to make the initial efforts worthwhile
So far in the PA the financial incentives are distributedamong the employees following a hierarchical mechanismwithout considering the performance of each employeeSpecifically the incentives are first uniformly distributedamong the business units and then subdivided among in-dividual employees e portion of incentives received byeach employee is proportional to its tenure ie related to therole in the organization not determined by its performance
As mentioned in the introduction the Italian DL15009tried to introduce a merit logic in the distribution ofmonetary incentives in the PA According to the DL15009the bonus is evaluated with a merit logic which is formalizedby the closed rank tournament theory which means that theemployees are ranked and only a subset takes the monetaryincentives according to the employeesrsquo performanceAccording to this law the employees are divided in three setscalled set A B and C and receive a different amount ofmonetary incentives according to the set In particular 25of the total employees is collocated in set A 50 in set B and25 in set C e total amount of monetary incentives isdivided as follows 50 to set A 50 to set B and 0 to setC us people in set C do not receive any kind of monetaryincentives
e main research question of the paper is to investigateif the monetary incentives distributed according to meritcriteria ie according to DL 15009 are a stimulus forbetter performance in the short middle and long term eeffect of the introduction of DL15009 is investigatedconsidering the sustainability of the new rules for the dis-tribution of incentives along time using the agent-basedsimulation e simulation verifies if the monetary incen-tives distributed with merit criteria have positive or negative
effect after the introduction of the rule In detail the sus-tainability of the merit criteria in the distribution of mon-etary incentives is investigated considering how manyemployees every year are in the same set and how manyemployees change set trying to improve their performance
3 The Data
A series of interviews has been arranged in order to explorethe connection between the performance of the employeesand the allocation of economic incentives in February 2011131 employees were interviewed and in January 2013 thearranged interviews were 126 e interviews consisted ofone hour face-to-face sessions composed of 57 questions towhich the employees had to respond with a value between 1and 7 according to the Likert scale [80] e employeesinterviewed belong to five different organizational areas Inorder to minimize misunderstandings the research teamdirectly administered the questionnaires e questionnaireswere anonymous the provided data were only used forprivate purposes and the people were interviewed inagreement with the trade unions In February 2011 126questionnaires were collected out of 131 (four employeeswere absent in that period and one was hired as a temporarysecretary) In 2013 interviewees were 123 out of a total of126 e total number of employees decreased because therehave been a few retirements and due to the financial crisisthe assumption rate was lower than the retirement rate equestionnaires were composed of four different sections
(i) Personal data (gender and age)(ii) Position (tenure and organizational area)(iii) Skills (problem solving teamwork determination
customer oriented and self-organization)(iv) Intraorganization relationship
e resultant set of data provides information on bothemployee characteristics (occupied position knowledgeskills and background) and the organizational model (therelationships maintained between employees of the sameorganization and between different organizations) In ad-dition to this data the HR department provided the salaryinformation of employees for the three years from 2010 to2012 Specifically this information included
(i) e uniformly distributed portion of the bonusgranted to every employee
(ii) e portion of the bonus based on the criteria ofmerit
(iii) e salary-level there are 12 levels 8 of which arereserved for employees having nonexecutivepositions
It is worth noting that in 2010 the total amount ofincentives distributed equally among the business units was47 and the one distributed according the merit criteria was53 whereas in 2011 the allocation was 36 and 64respectively us the monetary incentives distributedaccording the merit criteria increases from 53 to 64
Complexity 3
4 The Model
41 e Network e employees in the model are orga-nized as a directed graph where the employees are thenodes and the arrows represent the interactions amongemployees e total number of employees is N and eachemployee is characterized by an identification number idAn employee is linked to a set of other employees whosenumber and strength (of the connection) gij depends onthe real data e connections among the employees havebeen determined ignoring the vertical relation amongsupervisors and employees and considering the informalnetwork created by means of the information obtainedwith the administered questionnaire In fact employeeswere asked with whom and how many times they need tointeract to perform the given task In particular they hadto indicate up to ten members of the organization theyneed to relate more directly and more frequently with inorder to improve or facilitate the execution of their ac-tivities In order to quantify the frequency of the con-nection ie the strength a Likert scale that ranges from 1(contacts infrequent some once a month) to 7 (severaltimes per day) has been used With the collected infor-mation an adjacency squared and not symmetricalmatrix has been built and shown in the informal networkof Figure 1 It is worth remarking that only the con-nections between employees in the same level have beenconsidered to find out only the ldquohorizontalrdquorelationships
e interactions in the graph are assumed to be uni-directional (ie if employee j influences employee i it doesnot necessarily mean that employee i influences employee j)and characterized by a weight gji assumed a positive realnumber in the range [0 1] proportional to the Likert scaleAs a directed graph is used both an output and input nodedegrees are defined e output node degree is associated tothe output branches of a given node whereas the input nodedegree is related to the input arrows
Furthermore each employee is characterized by herhisrank r and herhis performance P
At each time step h the performance of employee i isevaluated and the rank rh
i is updatede agentrsquos rank r is aninteger number between 1 and 3 depending on the set towhich the employee belongs Employees in set A have rankrh
i 1 in set B have rank rhi 2 and in set C have rank
rhi 3 According to their performance in descending orderthe employees are divided in three set A B and C Set A isformed by the top 25 of the total employees set B by thenext 50 and set C by the last 25 (see DL 15009 formore details) It is worth remembering that employeesbelonging to different sets receive a different fraction ofmonetary incentives In particular half of the total amountof monetary incentives is divided among employees in set Ahalf among employees in set B and 0 among employees inset C
e graph is responsible for the changes in employeesrsquorank In fact at each time step employees depending ontheir rank change a fraction of hisher connections in orderto improve the performance
42 e Performance As already stated in Section 2 theperformance is a function of Ability and Motivationsand quantitatively the performance is measured asthe production of ability and motivation [43] Informulas
Performance Ability times Motivation (1)
421 Ability As already stated in Section 2 in order todetect the abilities of employees the objective evaluationshave been considered by using the network analysis ap-proach Generally speaking the influence of an individualregarding other individuals within a network is indicated byhisher centrality [81]
Centrality in the advice network means the recognitiongiven to a single employee from herhis colleagues for theavailability in exchanging advices and in problem solving Acentral individual can increase knowledge about differentproblems over the years and as more and more colleaguesbecome dependent on herhim for some help shehe gainspower and authority [82 83] ere are many definitions ofcentrality but the most common are the Degree theCloseness the Betweenness the Coreness and the Bonacichcentrality [84ndash87]
In this paper among the others the degree centrality ischosen and the centrality is measured by means of thenumber of connections among the employees defining thecentrality index
e centrality index of employee i CIi indicates therelationship between employee i and the other employeesand in particular quantifies how employee i is involved inthe activities of the other employees
CIi TACi
cmax (2)
where TACi is the task advice centrality of employee i andcmax is the maximum number of input connections amongall the employees e task advice centrality for each nodeie the centrality of the individual in the social consultingnetwork is the sum of all incoming arrows (input nodedegree) multiplied by their weights As mentioned abovethe employeersquos centrality in the intraorganizational net-work reflects herhis skills to participate in working lifeand in particular indicates how a node is necessary toperform the employeesrsquo activities us it is a proxy of theemployeesrsquo ability In the formula the task advice cen-trality of employee i (TACi) is
TACi 1113944j
cjigji (3)
where cji are the incoming arrows of employee i and gji arethe respective weights
422 Motivation As stated in Section 2 the expectancytheory of motivation has been considered According to thistheory employees can be motivated if they believe that thereis a positive correlation between efforts and performanceis behavior has been schematized defining the motivation
4 Complexity
index MI In particular the motivation of employee i isquantified with the motivation index MIi According to DL15009 the employees are ranked and divided in three sets AB and C and receive a different fraction of monetary in-centive In particular 25 of the total employees is collo-cated in set A 50 in set B and 25 in set C respectivelywhereas half of the total amount of monetary incentives isdivided among employees in set A half among employees inset B and 0 among employees in set Cemotivation indexquantifies the motivation of each employee to do better inorder to receive more monetary incentive According to thedeprivation-satiation proposition the more often in therecent past a person has received a major award the less hewill confer a value to any further reward Following thisproposition for employees in set A (corresponding to highincentives) the motivation decreases increasing the per-formance evaluation and conversely for employees in set Cthe motivation increases if performance evaluation in-creases In particular the employees near the upper bound ofset A and the lower bound of set C are not motivated to dobetter [88] In the formula the motivation index MIA in setA is
MIA Es minus P
11138681113868111386811138681113868111386811138681113868
Es minus Ta( 1113857 (4)
where Es is the maximum value of performance in set A Ta
the minimum value of performance in set A P is the em-ployee performance and the motivation index in set C andMIC is
MIC P minus Ei
11138681113868111386811138681113868111386811138681113868
Tb minus Ei( 1113857 (5)
where Ei is the minimum value of rank in set C and Tb themaximum value of rank in set C For employees in set B themotivation is high when the employee is near the twobounds of the range and decreases in the middle is is inline with the theory that while choosing among differentactions an employee chooses the one for which the resultsmultiplied by the probability of getting it is greater [88]
MIB Tmb minus P
11138681113868111386811138681113868111386811138681113868
Ta minus Tb( 11138572 (6)
where Tmb is the middle value of rank in set B Table 1summarizes the parameters abbreviations
Figure 2 shows how the motivation index MI rangesalong the set A B and C
Employees in set A increase their motivation movingtheir level of assessment from Es (maximum level of as-sessment) to Ta Employees in set C decrease their moti-vation moving their level of assessment from Tb to Ei
Figure 1 Network of employees at time t 0
Complexity 5
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
4 The Model
41 e Network e employees in the model are orga-nized as a directed graph where the employees are thenodes and the arrows represent the interactions amongemployees e total number of employees is N and eachemployee is characterized by an identification number idAn employee is linked to a set of other employees whosenumber and strength (of the connection) gij depends onthe real data e connections among the employees havebeen determined ignoring the vertical relation amongsupervisors and employees and considering the informalnetwork created by means of the information obtainedwith the administered questionnaire In fact employeeswere asked with whom and how many times they need tointeract to perform the given task In particular they hadto indicate up to ten members of the organization theyneed to relate more directly and more frequently with inorder to improve or facilitate the execution of their ac-tivities In order to quantify the frequency of the con-nection ie the strength a Likert scale that ranges from 1(contacts infrequent some once a month) to 7 (severaltimes per day) has been used With the collected infor-mation an adjacency squared and not symmetricalmatrix has been built and shown in the informal networkof Figure 1 It is worth remarking that only the con-nections between employees in the same level have beenconsidered to find out only the ldquohorizontalrdquorelationships
e interactions in the graph are assumed to be uni-directional (ie if employee j influences employee i it doesnot necessarily mean that employee i influences employee j)and characterized by a weight gji assumed a positive realnumber in the range [0 1] proportional to the Likert scaleAs a directed graph is used both an output and input nodedegrees are defined e output node degree is associated tothe output branches of a given node whereas the input nodedegree is related to the input arrows
Furthermore each employee is characterized by herhisrank r and herhis performance P
At each time step h the performance of employee i isevaluated and the rank rh
i is updatede agentrsquos rank r is aninteger number between 1 and 3 depending on the set towhich the employee belongs Employees in set A have rankrh
i 1 in set B have rank rhi 2 and in set C have rank
rhi 3 According to their performance in descending orderthe employees are divided in three set A B and C Set A isformed by the top 25 of the total employees set B by thenext 50 and set C by the last 25 (see DL 15009 formore details) It is worth remembering that employeesbelonging to different sets receive a different fraction ofmonetary incentives In particular half of the total amountof monetary incentives is divided among employees in set Ahalf among employees in set B and 0 among employees inset C
e graph is responsible for the changes in employeesrsquorank In fact at each time step employees depending ontheir rank change a fraction of hisher connections in orderto improve the performance
42 e Performance As already stated in Section 2 theperformance is a function of Ability and Motivationsand quantitatively the performance is measured asthe production of ability and motivation [43] Informulas
Performance Ability times Motivation (1)
421 Ability As already stated in Section 2 in order todetect the abilities of employees the objective evaluationshave been considered by using the network analysis ap-proach Generally speaking the influence of an individualregarding other individuals within a network is indicated byhisher centrality [81]
Centrality in the advice network means the recognitiongiven to a single employee from herhis colleagues for theavailability in exchanging advices and in problem solving Acentral individual can increase knowledge about differentproblems over the years and as more and more colleaguesbecome dependent on herhim for some help shehe gainspower and authority [82 83] ere are many definitions ofcentrality but the most common are the Degree theCloseness the Betweenness the Coreness and the Bonacichcentrality [84ndash87]
In this paper among the others the degree centrality ischosen and the centrality is measured by means of thenumber of connections among the employees defining thecentrality index
e centrality index of employee i CIi indicates therelationship between employee i and the other employeesand in particular quantifies how employee i is involved inthe activities of the other employees
CIi TACi
cmax (2)
where TACi is the task advice centrality of employee i andcmax is the maximum number of input connections amongall the employees e task advice centrality for each nodeie the centrality of the individual in the social consultingnetwork is the sum of all incoming arrows (input nodedegree) multiplied by their weights As mentioned abovethe employeersquos centrality in the intraorganizational net-work reflects herhis skills to participate in working lifeand in particular indicates how a node is necessary toperform the employeesrsquo activities us it is a proxy of theemployeesrsquo ability In the formula the task advice cen-trality of employee i (TACi) is
TACi 1113944j
cjigji (3)
where cji are the incoming arrows of employee i and gji arethe respective weights
422 Motivation As stated in Section 2 the expectancytheory of motivation has been considered According to thistheory employees can be motivated if they believe that thereis a positive correlation between efforts and performanceis behavior has been schematized defining the motivation
4 Complexity
index MI In particular the motivation of employee i isquantified with the motivation index MIi According to DL15009 the employees are ranked and divided in three sets AB and C and receive a different fraction of monetary in-centive In particular 25 of the total employees is collo-cated in set A 50 in set B and 25 in set C respectivelywhereas half of the total amount of monetary incentives isdivided among employees in set A half among employees inset B and 0 among employees in set Cemotivation indexquantifies the motivation of each employee to do better inorder to receive more monetary incentive According to thedeprivation-satiation proposition the more often in therecent past a person has received a major award the less hewill confer a value to any further reward Following thisproposition for employees in set A (corresponding to highincentives) the motivation decreases increasing the per-formance evaluation and conversely for employees in set Cthe motivation increases if performance evaluation in-creases In particular the employees near the upper bound ofset A and the lower bound of set C are not motivated to dobetter [88] In the formula the motivation index MIA in setA is
MIA Es minus P
11138681113868111386811138681113868111386811138681113868
Es minus Ta( 1113857 (4)
where Es is the maximum value of performance in set A Ta
the minimum value of performance in set A P is the em-ployee performance and the motivation index in set C andMIC is
MIC P minus Ei
11138681113868111386811138681113868111386811138681113868
Tb minus Ei( 1113857 (5)
where Ei is the minimum value of rank in set C and Tb themaximum value of rank in set C For employees in set B themotivation is high when the employee is near the twobounds of the range and decreases in the middle is is inline with the theory that while choosing among differentactions an employee chooses the one for which the resultsmultiplied by the probability of getting it is greater [88]
MIB Tmb minus P
11138681113868111386811138681113868111386811138681113868
Ta minus Tb( 11138572 (6)
where Tmb is the middle value of rank in set B Table 1summarizes the parameters abbreviations
Figure 2 shows how the motivation index MI rangesalong the set A B and C
Employees in set A increase their motivation movingtheir level of assessment from Es (maximum level of as-sessment) to Ta Employees in set C decrease their moti-vation moving their level of assessment from Tb to Ei
Figure 1 Network of employees at time t 0
Complexity 5
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
index MI In particular the motivation of employee i isquantified with the motivation index MIi According to DL15009 the employees are ranked and divided in three sets AB and C and receive a different fraction of monetary in-centive In particular 25 of the total employees is collo-cated in set A 50 in set B and 25 in set C respectivelywhereas half of the total amount of monetary incentives isdivided among employees in set A half among employees inset B and 0 among employees in set Cemotivation indexquantifies the motivation of each employee to do better inorder to receive more monetary incentive According to thedeprivation-satiation proposition the more often in therecent past a person has received a major award the less hewill confer a value to any further reward Following thisproposition for employees in set A (corresponding to highincentives) the motivation decreases increasing the per-formance evaluation and conversely for employees in set Cthe motivation increases if performance evaluation in-creases In particular the employees near the upper bound ofset A and the lower bound of set C are not motivated to dobetter [88] In the formula the motivation index MIA in setA is
MIA Es minus P
11138681113868111386811138681113868111386811138681113868
Es minus Ta( 1113857 (4)
where Es is the maximum value of performance in set A Ta
the minimum value of performance in set A P is the em-ployee performance and the motivation index in set C andMIC is
MIC P minus Ei
11138681113868111386811138681113868111386811138681113868
Tb minus Ei( 1113857 (5)
where Ei is the minimum value of rank in set C and Tb themaximum value of rank in set C For employees in set B themotivation is high when the employee is near the twobounds of the range and decreases in the middle is is inline with the theory that while choosing among differentactions an employee chooses the one for which the resultsmultiplied by the probability of getting it is greater [88]
MIB Tmb minus P
11138681113868111386811138681113868111386811138681113868
Ta minus Tb( 11138572 (6)
where Tmb is the middle value of rank in set B Table 1summarizes the parameters abbreviations
Figure 2 shows how the motivation index MI rangesalong the set A B and C
Employees in set A increase their motivation movingtheir level of assessment from Es (maximum level of as-sessment) to Ta Employees in set C decrease their moti-vation moving their level of assessment from Tb to Ei
Figure 1 Network of employees at time t 0
Complexity 5
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
(minimum level of assessment) Finally in set B employeesrsquomotivation tends to increase as their level of assessment isclose to Ta and Tb and is minimum at the midpoint of therange Tmb
en employee i has a motivation MIAi if his rank valuebelongs to set A MIBi if it belongs to set B and MICi if itbelongs to set C
423 Performance Calculus In the model the ability isapproximated quantitatively with the centrality index (CI)which considers the relations among the employees ie theinformal network whereas the motivation with the moti-vation index (MI)
us the performance of employee i is evaluated asfollows
Pi CIi times MIi (7)
where CIi is the centrality index and MIi the motivationindex It is worth remarking that the performance is con-sidered as the product of centrality index (that is a proxy ofability) and motivation index (that is a proxy of motivation)
5 Computational Experiments
In the computational experiments the number of agentsconsidered is 110 Figure 1 shows the network of employeesat time t 0 which corresponds to the empirical data
whereas Figure 3 zooms the connections of employee 61 attime t 0
e simulation duration is twenty years (T 20) inorder to consider the short middle and long termAccording to the empirical data the number of ranks isthree e strength of each connection gij between twoemployees is a real number in the range [0 1] e numberof employees in set A is fixed to 35 in set B to 70 and in set Cto 5 whereas the total amount of incentives is divided in 47for employees in set A 52 for employees in set B and 1for employees in set C It is worth noting that these values aredifferent from the ones defined by DL15009 because in thecomputational experiments the used values correspond tothe empirical data Table 2 summarizes the parameters usedin the simulations
At each time step that corresponds to a year employeeswith rank 1 2 and 3 change randomly from a uniformdistribution 10 20 and 30 of their connections re-spectively is assumption mimics the realistic behavior ofemployees in fact employees in set C change more con-nections than employees in set A and B because in order toimprove the performance they contact new employeeswhereas employees in set A change very few connectionsbecause they do not need to contact new employees toimprove their performance Figures 4ndash7 show in the top therank story and in the bottom the performance of agent 9103 119 and 108 during the simulation exhibiting thedifferent behaviors of employees
Figure 4 shows an employee who does not change hisherrank during the twenty years In this case the monetaryincentives system does not work as stimulus to improve hisher performance Figure 5 shows the rank behavior of anemployee that is not able to improve hisher performanceie the performance worsens and also in this case theincentivesrsquo systems does not work whereas Figure 6 showsthe rank behavior of an employee who is able to improve hisher performance and therefore in this case the incentivesrsquosystems work Finally Figure 7 shows the rank behavior ofan employee with positive and negative changes Also in thiscase the incentivesrsquo systems work as stimulus to improve theemployeesrsquo performance
Figure 8 shows the percentage of employees with dif-ferent behaviors during the simulation
In particular the blue circle line represents the per-centage of employees who are in set A the red dashed linethe ones in set B and the black stair line the ones in set Cwho did not change set during the twenty years e greentriangle line represents the percentage of employees whoduring the twenty years worsened or not improved theirrank position whereas the cyan diamond line represents theones who have improved or not worsened Finally themagenta continuous line represents the percentage of em-ployees who during the simulation time improved orworsened their position It is worth noting that the per-centage of employees who did not change set along thetwenty years decreases whereas the number of employeeswho did not improve and the ones who did not worsen isconstant Instead the percentage of employees who some-time improved and sometime worsened their rank increases
Table 1 Description of the simulation modelrsquos parameters
Abbreviation ParameterCI Network centrality indexMI Motivation indexEs Upper bound of set ATma Middle value of set ATa Lower bound of set A and upper bound of set BTmb Middle value of set BTb Lower bound of set B and upper bound of set CEi Lower bound of set CP Performance
Ei Tb Tmb Ta ESC B A
Lowerbound Upper bound
MI
MI_max
Figure 2 Motivation index
6 Complexity
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
along the twenty years is means that in the short termpeople think that changes in the PA cannot be possible asshown by the number of employees fixed in a set whereas inthe middle and long term the incentive system works be-cause employees who try to improve their performanceincrease and the number of employees who are fixed in a setdecreases
Table 3 underlies the rank story of the employees in thesimulation analysis T 20
Figure 9 shows the percentage of employees for whichthe monetary incentivesrsquo mechanism works and did notwork during the twenty years e blue circle line representsthe employees who are fixed in a set and the one that worsentheir rank position For these employees the incentivesrsquosystem does not work e red stair line represents theemployees who increase or increase and decrease their rankposition For these employees the incentivesrsquo system worksIt is worth noting that starting from year 12 (middle term)the percentage of employees which believes in the incentivesrsquomechanism is larger than the one which does not Moreoverthis result confirms that the incentives distributed accordingto a merit approach bring to a better performance of em-ployees and then of the firm in the middle and long term
Finally Figure 10 shows the analysis in the very shortterm considering the behavior of employees rank andperformance from year t minus 1 and t
Figure 10(a) shows that from year t minus 1 and t thepercentage of employees which does not change rank isbetween 85 and 95 whereas the number of employeeswhich improves and the one which worsens rank is between5 and 15 in both cases whereas Figure 10(b) shows thatthe percentage of employees which does not change theirperformance is between 1 and 15 whereas the number ofemployees which improves and the one which worsens theirperformance is around 50 in both cases is means thateven if in the short term the number of employees whichdoes not change rank is very large the number of employeeswhich does not change their performance is very fewshowing that the employees try to improve also in the shortterm even if the results is visible only in the middle and longterm In the very short term employees move their per-formance but this is not visible from the rank
Finally the analysis shows that the monetary incentivesdistributed according to a merit logic and the performanceare linked in particular in the middle and long term sim-ulation In fact in the middle and long term the number ofemployees which does not change their rank decreasesconfirming the positive effect of the incentives distributedwith merit criteria is means that the employees considerthe incentives a good motivation for better performingMoreover in the short and very short term the resultssuggest that from a macropoint of view the employees thinkthat changes in the PA are very difficult but a deeper analysisshows that the employeesrsquo performance changes meaningwhich they try to improve in order to get a larger incentive Itis worth noting that the incentives distributed with meritlogic bring the employees to a better individual performanceand then to a better firmrsquos performanceus the hypothesisis confirmed in fact after n-step people continue to try toimprove their performance
6 Empirical Analysis
e computational results are confirmed in the short term bythe empirical analysis on real data Table 4 shows the sameanalysis performed for the computational experiments forthe real data In particular the number of employees whichis always in set A B or C and the ones which always worsensor improves or worseimprove their rank in year 20102011and 20102012 are reported
e results confirm the decreasing number of employeesin a fixed set and the increasing number of the employeeswhich improves and worsens their rank position enumber of employees which always improves or worsensremain more or less constant
Concerning the very short term Tables 5 and 6 show theemployeesrsquo rank and performance in the period 20102011and 20112012 e results confirm the computational ex-periments results
7 Discussion and Conclusions
In this paper the distribution of monetary incentives in thePA through a rank order tournament has been addressede relationship between the monetary incentives and
Figure 3 Zoom of connections of employee 61 at time t 0
Table 2 e most relevant parameter values used in thesimulation
Symbol Description ValueN Number of employees 110NA Number of employees in set A 35NB Number of employees in set B 70NC Number of employees in set C 5T Duration of simulation (years) 20R Number of rank 3gij Strength of connections [0 1]
Complexity 7
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
performance of employees has been studied by mean of anempirical and computational approach According to theclassical literature the proposed model incorporates twovariables the motivation and the ability In particular theemployeesrsquo performance has been evaluated multiplying themotivation and the ability components and the incentiveshave been distributed according to DL15009 (the mone-tary incentives are divided among the employees with a logicthat consider the employeesrsquo performance) e design of
both employeesrsquo performance evaluation and monetaryincentives distribution have been presented and discussedaccording to the theoretical and computational aspects
e results have shown a modification of the employeersquosbehavior according to both the theoretical foundations andthe results discussed in [89 90] Both the empirical andcomputational results show that the monetary incentiveswork as stimulus for employees to reach the maximumincentive and the mechanism is suitable during the years It
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 4 Rank history (a) and performance (b) of agent 9 During the simulation the employee 9 does not change hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 5 Rank history (a) and performance (b) of agent 103 During the simulation the employee 103 worsens hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 6 Rank history (a) and performance (b) of agent 119 During the simulation the employee 119 improves hisher rank
Years
0
2
4
Rank
0 5 10 15 20
(a)
0 5Years
0
5
10
15
Perfo
rman
ce
10 15 20
(b)
Figure 7 Rank history (a) and performance (b) of agent 108 During the simulation the employee 108 changes hisher rank
8 Complexity
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
is worth noting that with the use of a rank order tournamentmechanism that is an ordinal system to evaluate the per-formance of single employees the result of the evaluation isknown only at the end is meritocratic system increasesemployee reactivity to managersrsquo incitation as suggested by
the theory of social exchange [88] Moreover as discussed in[91 92] the model implemented fits the fundamentals of avirtuous use of monetary incentives such as the legitimacyof the appraisal the objectivity of the criteria and thepossibility to achieve the initial goals at each repetition of the
Years
0
10
20
30
40
50
60
o
f em
ploy
ees
2 4 6 8 10 14 16 1812
Figure 8 Percentage of employees with different behaviors during the simulation e blue circle line represents the percentage ofemployees who are in set A the red dashed line represents the ones in set B and the black stair line represents the ones in set C who did notchange set during the twenty yearse green triangle line represents the percentage of employees who during the twenty years worsened ornot improved their rank position whereas the cyan diamond line represents the ones who improved or not worsened e magentacontinuous line represents the percentage of employees who during the simulation time improved or worsened their position
Table 3 Rank story of the employees Number of employees who changed or did not change their rank during the twenty years simulation
Employeesrsquo set T1 T 2 T 3 T 4 T 5 T10 T15 T19A 33 31 30 30 29 26 23 21B 68 66 65 65 64 58 56 54C 5 5 5 5 5 2 2 2Worsening rank 2 4 5 5 6 12 14 16Improving rank 2 4 5 5 6 12 13 15Worseningimproving 0 0 0 0 0 0 2 2
Years
0
20
40
60
80
100
o
f em
ploy
ees
2 4 6 8 10 12 14 16 18
Figure 9 Percentage of employees for which the incentivesrsquo mechanism works in red star line and does not work in blue circle line
Complexity 9
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
tournament Furthermore a study about various publiccompanies in Britain has confirmed that employeesrsquo moti-vation is reduced if performance-based pay does not operatefairly [93] Finally results have shown that the monetaryincentives distributed with a merit logic impact positivelythe firm performance in the short middle and long termemain limitation of the study is that only one local PA hasbeen considered to calibrate the model In the near futureother PA will be considered to enrich the analysis and thesimulation model e developed agent-based model andsimulator where agents represent the employees are one ofthe first attempts to provide a suitable tool to make
managerial analysis In particular policy makers can use thedeveloped tool to experiment different monetary incentivesmechanisms in order to find the most convenient policy thatallows to enhance the employee performance In the end it isworth remembering that the developed simulator is a usefultool not only for Public Administrations but also for privatecompanies
Data Availability
Personnel questionnaire data are subject to NDA and cannotbe provided Simulation data can be provided upon request
Conflicts of Interest
e authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
e authors gratefully acknowledge Camera di Commerciodi Genova for useful discussions
References
[1] C Pollitt and G Bouckaert Public Management Reform AComparative Analysis Oxford University Press Oxford UK2004
[2] M Barzelay Breaking through Bureaucracy A New Vision forManaging in Government University of California PressBerkeley CA USA 1992
[3] N Flynn Public Sector Management Sage ousand OaksCA USA 2007
[4] W J Kickert E-H Klijn and J F M Koppenjan ManagingComplex Networks Strategies for the Public Sector Sageousand Oaks CA USA 1997
[5] C Hood ldquoA public management for all seasonsrdquo PublicAdministration vol 69 no 1 pp 3ndash19 1991
[6] C Hood ldquoe ldquonew public managementrdquo in the 1980svariations on a themerdquo Accounting Organizations and So-ciety vol 20 no 2-3 pp 93ndash109 1995
[7] G Gruening ldquoOrigin and theoretical basis of new publicmanagementrdquo International Public Management Journalvol 4 no 1 pp 1ndash25 2001
[8] J Valasek ldquoDynamic reform of public institutions a model ofmotivated agents and collective reputationrdquo Journal of Publicvol 168 pp 94ndash108 2018
2 4 6 8Years
0
50
100
of e
mpl
oyee
s
10 12 14 16 18
(a)
0
50
100
o
f em
ploy
ees
2 4 6 8Years
10 12 14 16 18
(b)
Figure 10 (a) of employees which does not change rank from t minus 1 to t in blue circle line of employees which improves rank positionfrom t minus 1 to t in black dashed and of employees which worsens rank position from t minus 1 to t in red star line (b) of employees whichdoes not change their performance from t minus 1 to t in blue circle line of employees which improves their performance from t minus 1 to t inblack dashed and of employees which worsens their performance from t minus 1 to t in red star line
Table 4 Rank story of the employees in the real case Number ofemployees which changes or does not change their rank during theperiods 20102011 and 20102012
Employeesrsquo set 20102011 20102012A 26 23B 60 53C 3 3Worsening rank 11 14Improving rank 12 12Worseningimproving 0 7
Table 5 Rank story of the employees (real data) Number ofemployees which changes or does not change their rank duringyears 20102011 and 20112012
Employeesrsquo rank 20102011 20112012Fixed rank 89 95Worsening rank 11 10Improving rank 12 7
Table 6 Performance story of the employees (real data) Numberof employees which changes or does not change their performanceduring years 20102011 and 20112012
Employeesrsquo performance 20102011 20112012Fixed performance 31 42Improving performance 44 46Worsening performance 37 24
10 Complexity
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
[9] A B Whitford ldquoIncentives and tournaments in public or-ganizationsrdquo 2006 httpsssrncomabstract=873488
[10] T Eriksson andM C Villeval ldquoPerformance-pay sorting andsocial motivationrdquo Journal of Economic Behavior amp Organi-zation vol 68 no 2 pp 412ndash421 2008
[11] L Ponta A Carbone and M Gilli ldquoResistive transition indisordered superconductors with varying intergrain cou-plingrdquo Superconductor Science amp Technology vol 24 no 1Article ID 015006 2011
[12] A Teglio A Mazzocchetti L Ponta M Raberto andS Cincotti ldquoBudgetary rigour with stimulus in lean timespolicy advices from an agent-based modelrdquo Journal of Eco-nomic Behavior amp Organization vol 157 pp 59ndash83 2019
[13] M Raberto B Ozel L Ponta A Teglio and S CincottildquoFrom financial instability to green finance the role ofbanking and credit market regulation in the Eurace modelrdquoJournal of Evolutionary Economics vol 29 no 1 pp 429ndash4652019
[14] J P Davis K M Eisenhardt and C B Bingham ldquoDevelopingtheory through simulation methodsrdquo Academy of Manage-ment Review vol 32 no 2 pp 480ndash499 2007
[15] D C Smith ldquoMaking management count a case for theory-and evidence-based public managementrdquo Journal of PolicyAnalysis And Management vol 28 no 3 pp 497ndash505 2009
[16] L Iandoli E Marchione C Ponsiglione and G ZolloldquoLearning and structural properties in small firmsrsquo networks acomputational agent-based modelrdquo Research in Economicsand Business Central and Eastern Europe vol 1 2013
[17] L Fraccascia I Giannoccaro and V Albino ldquoEfficacy oflandfill tax and subsidy policies for the emergence of in-dustrial symbiosis networks an agent-based simulationstudyrdquo Sustainability vol 9 no 4 p 521 2017
[18] T Wu S Huang J Blackhurst X Zhang and S WangldquoSupply chain risk management an agent-based simulation tostudy the impact of retail stockoutsrdquo IEEE Transactions onEngineering Management vol 60 no 4 pp 676ndash686 2013
[19] M A Zaffar R L Kumar and K Zhao ldquoImpact of inter-organizational relationships on technology diffusion anagent-based simulation modeling approachrdquo IEEE Transac-tions on Engineering Management vol 61 no 1 pp 68ndash792014
[20] A F de Toni and F Nonino ldquoe key roles in the informalorganization a network analysis perspectiverdquo e LearningOrganization vol 17 no 1 pp 86ndash103 2010
[21] S Pastore L Ponta and S Cincotti ldquoHeterogeneous infor-mation-based artificial stock marketrdquo New Journal of Physicsvol 12 no 5 Article ID 053035 2010
[22] L Ponta S Pastore and S Cincotti ldquoInformation-basedmulti-assets artificial stock market with heterogeneousagentsrdquo Nonlinear Analysis Real World Applications vol 12no 2 pp 1235ndash1242 2011
[23] L Ponta M Raberto and S Cincotti ldquoA multi-assets artificialstockmarket with zero-intelligence tradersrdquo EPL (EurophysicsLetters) vol 93 no 2 p 28002 2011
[24] L Ponta E Scalas M Raberto and S Cincotti ldquoStatisticalanalysis and agent-based microstructure modeling of high-frequency financial tradingrdquo IEEE Journal of Selected Topics inSignal Processing vol 6 no 4 pp 381ndash387 2012
[25] L Ponta and S Cincotti ldquoTradersrsquo networks of interactionsand structural properties of financial markets an agent-basedapproachrdquo Complexity vol 2018 Article ID 9072948 9 pages2018
[26] L Ponta S Pastore and S Cincotti ldquoStatic and dynamicfactors in an information-based multi-asset artificial stock
marketrdquo Physica A Statistical Mechanics and Its Applicationsvol 492 pp 814ndash823 2018
[27] B Vermeulen and M Paier Innovation Networks for RegionalDevelopment Concepts Case Studies and Agent-BasedModels Springer Berlin Germany 2016
[28] R Axelrode Complexity of Cooperation Agent-asedModelsof Competition and Collaboration vol 3 Princeton UniversityPress Princeton NJ USA 1997
[29] R Axelrod ldquoChapter 33 agent-based modeling as a bridgebetween disciplinesrdquo Handbook of Computational Economicsvol 2 pp 1565ndash1584 2006
[30] J M Epstein Generative Social Science Studies in Agent-Based Computational Modeling Princeton University PressPrinceton NJ USA 2006
[31] N Gilbert and P Terna ldquoHow to build and use agent-basedmodels in social sciencerdquo Mind amp Society vol 1 no 1pp 57ndash72 2000
[32] A Pyka and T GrebelAgent-Based Computational ModellingSpringer Berlin Germany 2006
[33] M Wooldridge ldquoAgent-based computingrdquo InteroperableCommunication Networks vol 1 pp 71ndash98 1998
[34] D Helbing Social Self-Organization Agent-Based Simulationsand Experiments to Study Emergent Social Behavior SpringerBerlin Germany 2012
[35] B J L Berry L D Kiel and E Elliott ldquoAdaptive agentsintelligence and emergent human organization capturingcomplexity through agent-basedmodelingrdquo Proceedings of theNational Academy of Sciences vol 99 no 3 pp 7187-71882002
[36] J Grundspenkis ldquoAgent based approach for organization andpersonal knowledge modelling knowledge managementperspectiverdquo Journal of Intelligent Manufacturing vol 18no 4 pp 451ndash457 2007
[37] G Fioretti ldquoAgent-based simulation models in organizationsciencerdquo Organizational Research Methods vol 16 no 2pp 227ndash242 2013
[38] R D Behn ldquoe big questions of public managementrdquo PublicAdministration Review vol 55 no 4 pp 313ndash324 1995
[39] P M Wright T M Gardner and L M Moynihan ldquoeimpact of HR practices on the performance of business unitsrdquoHuman Resource Management Journal vol 13 no 3pp 21ndash36 2003
[40] M A Youndt S A Snell J W Dean and D P LepakldquoHuman resource management manufacturing strategy andfirm performancerdquo Academy of Management Journal vol 39no 4 pp 836ndash866 1996
[41] T Boland and A Fowler ldquoA systems perspective of perfor-mance management in public sector organisationsrdquo Inter-national Journal of Public Sector Management vol 13 no 5pp 417ndash446 2000
[42] S Brignall and S Modell ldquoAn institutional perspective onperformance measurement and management in the ldquonewpublic sectorrdquordquo Management Accounting Research vol 11no 3 pp 281ndash306 2000
[43] C A Mace ldquoIncentives Some experimental studiesrdquo In-dustrial Health Research Board Report Medical ResearchCouncil London UK 1935
[44] M S Viteles Motivation and Morale in Industry NYCNorton Jersey City NJ USA 1953
[45] N R F Maier Psychology in Industry A Psychological Ap-proach to Industrial Problems HoughtonMifflin Boston MAUSA 1955
Complexity 11
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
[46] E Appelbaum Manufacturing Advantage Why High-Per-formance Work Systems Pay Off Cornell University PressIthaca NY USA 2000
[47] J Paauwe ldquoHRM and performance achievements method-ological issues and prospectsrdquo Journal of ManagementStudies vol 46 no 1 pp 129ndash142 2009
[48] P Boxall and J Purcell ldquoStrategy and Human ResearchManagement Management Work and Organisations SeriesrdquoPalgrave Macmillan Basingstoke UK 2008
[49] J E Delery and J D Shaw ldquoe strategic management ofpeople in work organizations review synthesis and exten-sionrdquo in Research in Personnel and Human Resources Man-agement vol 20 pp 165ndash197 Emerald Group PublishingBingley UK 2001
[50] H C Katz T A Kochan and M R Weber ldquoAssessing theeffects of industrial relations systems and efforts to improvethe quality of working life on organizational effectivenessrdquoAcademy of Management Journal vol 28 no 3 pp 509ndash5261985
[51] D P Lepak H Liao Y Chung and E E Harden ldquoA con-ceptual review of human resource management systems instrategic human resource management researchrdquo in Researchin Personnel and Human Resources Management vol 25pp 217ndash271 Emerald Group Publishing Bingley UK 2006
[52] A H Brayfield and W H Crockett ldquoEmployee attitudes andemployee performancerdquo Psychological Bulletin vol 52 no 5pp 396ndash424 1955
[53] M Banno and F Sgobbi ldquoFirm participation in financialincentive programmes the case of subsidies for outwardinternationalisationrdquo Journal of Policy Modeling vol 32no 6 pp 792ndash803 2010
[54] L B Andersen ldquoProfessional norms public service motiva-tion and economic incentives what motivates public em-ployeesrdquo in Proceedings of the EGPA Conference 2007Department of Political Science University of AarhusMadrid Spain September 2007
[55] C Dahlstrom and V Lapuente Organizing Leviathan Poli-ticians Bureaucrats and the Making of Good GovernmentCambridge University Press Cambridge UK 2017
[56] E Chang ldquoMotivational effects of pay for performance amultilevel analysis of a Korean caserdquo e InternationalJournal of Human Resource Management vol 22 no 18pp 3929ndash3948 2011
[57] T Lah and J L Perry ldquoe diffusion of the Civil ServiceReform Act of 1978 in OECD countries a tale of two paths toreformrdquo Review of Public Personnel Administration vol 28no 3 pp 282ndash299 2008
[58] J E Salzman ldquoLabor rights globalization and institutions therole and influence of the Organization for Economic Coop-eration and Developmentrdquo SSRN Electronic Journal vol 21pp 769ndash975 2000
[59] R F Durant R Kramer J L Perry D Mesch andL Paarlberg ldquoMotivating employees in a new governance erathe performance paradigm revisitedrdquo Public AdministrationReview vol 66 pp 505ndash514 2006
[60] J L Pearce and J L Perry ldquoFederal merit pay a longitudinalanalysisrdquo Public Administration Review vol 43 no 4pp 315ndash325 1983
[61] B F Skinner ldquoContingencies of reinforcementrdquo Encyclopediaof Pain Springer Berlin Germany 1969
[62] F Luthans ldquoe contingency theory of managementrdquoBusiness Horizons vol 16 no 3 pp 67ndash72 1973
[63] A D Stajkovic and F Luthans ldquoA meta-analysis of the effectsof organizational behavior modification on task performance
1975ndash1995rdquo Academy of Management Journal vol 40 no 5pp 1122ndash1149 1997
[64] W Van Eerde and H ierry ldquoVroomrsquos expectancy modelsand work-related criteria a meta-analysisrdquo Journal of AppliedPsychology vol 81 no 5 pp 575ndash586 1996
[65] J S Adams Advances in Experimental Social PsychologyVol 2 Elsevier Amsterdam e Netherlands 1965
[66] J Greenberg ldquoOrganizational justice yesterday today andtomorrowrdquo Journal of Management vol 16 no 2 pp 399ndash432 1990
[67] J L Perry T A Engbers and S Y Jun ldquoBack to the futurePerformance-related pay empirical research and the perils ofpersistencerdquo Public Administration Review vol 69 no 1pp 39ndash51 2009
[68] S M Davidson L MManheim SMWerner MM HohlenB K Yudkowsky and G V Fleming ldquoPrepayment withoffice-based physicians in publicly funded programs resultsfrom the Childrenrsquos Medicaid Programrdquo Pediatrics vol 89no 89 pp 761ndash767 1992
[69] B Dowling and R Richardson ldquoEvaluating performance-related pay for managers in the national health servicerdquo eInternational Journal of Human Resource Management vol 8no 3 pp 348ndash366 1997
[70] J D Shaw M K Duffy A Mitra D E Lockhart andM Bowler ldquoReactions to merit pay increases a longitudinaltest of a signal sensitivity perspectiverdquo Journal of AppliedPsychology vol 88 no 3 pp 538ndash544 2003
[71] J Cilliers I Kasirye C Leaver P Serneels and A ZeitlinldquoPay for locally monitored performance A welfare analysisfor teacher attendance in Ugandan primary schoolsrdquo Journalof Public Economics vol 167 pp 69ndash90 2018
[72] N Belle and P Cantarelli ldquoMonetary incentives motivationand job effort in the public sectorrdquo Review of Public PersonnelAdministration vol 35 no 2 pp 99ndash123 2015
[73] G J Miller and A BWhitford ldquoe principalrsquos moral hazardconstraints on the use of incentives in hierarchyrdquo Journal ofPublic Administration Research and eory vol 17 pp 213ndash233 2006
[74] J A Marin-Garcia and J M Tomas ldquoDeconstructing AMOframework a systematic reviewrdquo Intangible Capital vol 12no 4 pp 1040ndash1087 2016
[75] L C Freeman ldquoA set of measures of centrality based onbetweennessrdquo Sociometry vol 40 no 1 pp 35ndash41 1977
[76] P Bonacich ldquoPower and centrality a family of measuresrdquoAmerican Journal of Sociology vol 92 no 5 pp 1170ndash11821987
[77] J W Atkinson ldquoMotivational determinants of risk-takingbehaviorrdquo Psychological Review vol 64 no 6 pp 359ndash3721957
[78] Y-Y Chen and W Fang ldquoe moderating effect of im-pression management on the organizational politics-perfor-mance relationshiprdquo Journal of Business Ethics vol 79 no 3pp 263ndash277 2008
[79] E Lawler L Porter and V Vroom Motivation and man-agement Vroomrsquos expectancy theory Value based managementwebsite httpswwwvaluebasedmanagementnetmethods_vroom_expectancy_theoryhtml 2009
[80] G Albaum ldquoe Likert scale revisitedrdquo Journal-Market Re-search Society vol 39 pp 331ndash348 1997
[81] D J Brass and M E Burkhardt ldquoCentrality and power inorganizationsrdquo Networks and Organizations Structure Formand Action vol 191 pp 198ndash213 1992
[82] T T Baldwin M D Bedell and J L Johnson ldquoe socialfabric of a team-based M B A Program network effects on
12 Complexity
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13
student satisfaction and performancerdquo Academy of Man-agement Journal vol 40 no 6 pp 1369ndash1397 1997
[83] K S Cook R M Emerson M R Gillmore and T Yamagishildquoe distribution of power in exchange networks theory andexperimental resultsrdquo American Journal of Sociology vol 89no 2 pp 275ndash305 1983
[84] R Aalbers and W Dolfsma Innovation Networks Managingthe Networked Organization Routledge Abingdon UK 2015
[85] L Lu T Zhou Q-M Zhang and H E Stanley ldquoe H-indexof a network node and its relation to degree and corenessrdquoNature Communications vol 7 no 1 p 10168 2016
[86] M Kitsak L K Gallos S Havlin et al ldquoIdentification ofinfluential spreaders in complex networksrdquo Nature Physicsvol 6 no 11 pp 888ndash893 2010
[87] J Boissevain and J C Mitchell Network Analysis Studies inHuman Interaction Walter de Gruyter GmbH amp Co KGBerlin Germany 2018
[88] G C Homans Social Behavior Its Elementary Forms RevisedEd Harcourt Brace and World Inc New York NY USA1974
[89] G C Cainarca F Delfino and L Ponta ldquoe effect ofmonetary incentives on individual and organizational per-formance in an Italian public institutionrdquo AdministrativeSciences vol 9 no 3 p 72 2019
[90] L Ponta F Delfino and G C Cainarca ldquoe role of monetaryincentives bonus andor stimulusrdquo Administrative Sciencesvol 10 no 1 p 8 2020
[91] C R Knoeber and W N urman ldquoTesting the theory oftournaments an empirical analysis of broiler productionrdquoJournal of Labor Economics vol 12 no 2 pp 155ndash179 1994
[92] S Rosen ldquoPrizes and incentives in elimination tournamentsrdquoAmerican Economic Review vol 76 no 4 pp 701ndash715 1986
[93] D Marsden and S French ldquoPerformance pay in the UnitedKingdomrdquo in Paying for Performance An InternationalComparison pp 115ndash147 ME Sharpe Armonk NY USA2002
Complexity 13