the symbiosis mechanism for effective knowledge transfer

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AUTHOR COPY Knowledge management strategy and organizational culture Sajjad M Jasimuddin 1 * and Zuopeng (Justin) Zhang 2 1 School of Management and Business, Aberystwyth University, Aberystwyth, Wales, UK; and 2 School of Business & Economics, State University of New York at Plattsburgh, New York, USA In an emerging knowledge-based economy, knowledge is a critical source of competitive advantage of organiza- tions. This paper addresses two different strategies based on the tacitness of knowledge, indicating how the dilemmas of the choice of knowledge strategies might be resolved. A successful symbiosis strategy based upon a conducive organizational culture can ease knowledge replication within the organization but presents difculty in imitation by competitors. Such a culture needs to be pervasive within the organization, but at the same time idio- syncratic and unique to the organization. Optimal knowledge management strategies can cultivate the organiza- tional cultural t, and maximize the organizational prot. The paper provides researchers and practitioners valuable insights to understand the fundamental relationship between knowledge management and organizational culture, and practical guidance to adopt an appropriate knowledge management strategy to exploit organizational knowledge. Journal of the Operational Research Society advance online publication, 4 September 2013; doi:10.1057/jors.2013.101 Keywords: knowledge management; tacit knowledge; explicit knowledge; strategy; organizational culture 1. Introduction In a knowledge-based economy, knowledge is regarded as the critical source of competitive advantage for organizations (Grant, 1996; Miller et al, 2007). Researchers and practitioners have shown interests in studying various issues surrounding knowledge management: typology of organizational knowledge (Polanyi, 1967; Blackler, 1995; Nonaka and Takeuchi, 1995; Jasimuddin et al, 2005), knowledge transfer (Szulanski, 1996; Jasimuddin et al, 2012), knowledge creation process (Nonaka and Takeuchi, 1995), and knowledge storage (Walsh and Ungson, 1991; Klein et al, 2007; Jasimuddin and Zhang, 2011). Nonaka (1994), for example, observes that knowledge is the single most important production factor in terms of the capacity of an organization to survive and, subsequently, the means of its gaining and sustaining competitive advantage. This is echoed by other scholars (eg, Grant, 1996; Drucker, 2000; Quinn et al, 2004). Among the authors, Drucker (1992, p 95) puts it: In this society, knowledge is the primary source for individuals and for the economy overall. Land, labor, and capitalthe economists traditional factors of productiondo not disappear, but they become secondary. Although the extant literature has focused on various issues relating to organizational knowledge, one question that still remains unresolved arises from the inuence of organizational culture on the utilization of tacit and explicit knowledge. This issue seems to be one of the key problems that organizations encounter, and that managers have to address. Parallel to this, Alavi et al (2005) contend that the issue of organizational culture is often cited as a signicant challenge in knowledge management practices. In particular, the strategic choice of making organizational knowledge more accessible is possible by converting tacit into explicit knowledge. This leads organi- zations to a dilemma: tacit knowledge is less vulnerable but less accessible by legitimate users, while explicit knowledge is more accessible but also more vulnerable to illegitimate exploitation by outsiders. Failure to recognize the implications of such issue may undermine organizational efforts to use knowledge more effectively in order to ensure sustainable competitive advantage. Our paper highlights the implications of knowledge manage- ment strategies for rms, indicating how the dilemmas of choice of knowledge strategies can be resolved. Essentially, our paper provides researchers and practitioners valuable insights to understand the fundamental relationship between organizational knowledge and organizational culture, and practical guidance in order to adopt an appropriate knowledge management strategy. The rest of our paper is organized as follows. The next section provides an extensive literature review. Section 3 presents our analytical model surrounding knowledge manage- ment and organizational culture. Section 4 details our analysis on optimal knowledge management strategies that cultivate the organizational cultural t, and maximize the organizational prot. Section 5 concludes the paper. *Correspondence: Sajjad M Jasimuddin, Department of Strategy and Environment, Kedge Business School, Marseille Campus, Marseille, 13288, France. E-mail: [email protected] Journal of the Operational Research Society (2013),111 © 2013 Operational Research Society Ltd. All rights reserved. 0160-5682/13 www.palgrave-journals.com/jors/

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Knowledge management strategy and organizationalcultureSajjad M Jasimuddin1* and Zuopeng (Justin) Zhang21School of Management and Business, Aberystwyth University, Aberystwyth, Wales, UK; and 2School ofBusiness & Economics, State University of New York at Plattsburgh, New York, USA

In an emerging knowledge-based economy, knowledge is a critical source of competitive advantage of organiza-tions. This paper addresses two different strategies based on the tacitness of knowledge, indicating how thedilemmas of the choice of knowledge strategies might be resolved. A successful symbiosis strategy based upon aconducive organizational culture can ease knowledge replication within the organization but presents difficulty inimitation by competitors. Such a culture needs to be pervasive within the organization, but at the same time idio-syncratic and unique to the organization. Optimal knowledge management strategies can cultivate the organiza-tional cultural fit, and maximize the organizational profit. The paper provides researchers and practitioners valuableinsights to understand the fundamental relationship between knowledge management and organizational culture,and practical guidance to adopt an appropriate knowledge management strategy to exploit organizationalknowledge.Journal of the Operational Research Society advance online publication, 4 September 2013; doi:10.1057/jors.2013.101

Keywords: knowledge management; tacit knowledge; explicit knowledge; strategy; organizational culture

1. Introduction

In a knowledge-based economy, knowledge is regarded as thecritical source of competitive advantage for organizations(Grant, 1996; Miller et al, 2007). Researchers and practitionershave shown interests in studying various issues surroundingknowledge management: typology of organizational knowledge(Polanyi, 1967; Blackler, 1995; Nonaka and Takeuchi, 1995;Jasimuddin et al, 2005), knowledge transfer (Szulanski, 1996;Jasimuddin et al, 2012), knowledge creation process (Nonakaand Takeuchi, 1995), and knowledge storage (Walsh andUngson, 1991; Klein et al, 2007; Jasimuddin and Zhang, 2011).Nonaka (1994), for example, observes that knowledge is thesingle most important production factor in terms of the capacityof an organization to survive and, subsequently, the means of itsgaining and sustaining competitive advantage. This is echoed byother scholars (eg, Grant, 1996; Drucker, 2000; Quinn et al,2004). Among the authors, Drucker (1992, p 95) puts it:

In this society, knowledge is the primary source for individualsand for the economy overall. Land, labor, and capital—theeconomist’s traditional factors of production—do not disappear,but they become secondary.

Although the extant literature has focused on various issuesrelating to organizational knowledge, one question that still

remains unresolved arises from the influence of organizationalculture on the utilization of tacit and explicit knowledge. Thisissue seems to be one of the key problems that organizationsencounter, and that managers have to address. Parallel to this,Alavi et al (2005) contend that the issue of organizationalculture is often cited as a significant challenge in knowledgemanagement practices. In particular, the strategic choice ofmaking organizational knowledge more accessible is possibleby converting tacit into explicit knowledge. This leads organi-zations to a dilemma: tacit knowledge is less vulnerable but lessaccessible by legitimate users, while explicit knowledge is moreaccessible but also more vulnerable to illegitimate exploitationby outsiders. Failure to recognize the implications of such issuemay undermine organizational efforts to use knowledge moreeffectively in order to ensure sustainable competitive advantage.Our paper highlights the implications of knowledge manage-ment strategies for firms, indicating how the dilemmas of choiceof knowledge strategies can be resolved. Essentially, our paperprovides researchers and practitioners valuable insights tounderstand the fundamental relationship between organizationalknowledge and organizational culture, and practical guidance inorder to adopt an appropriate knowledge management strategy.The rest of our paper is organized as follows. The next

section provides an extensive literature review. Section 3presents our analytical model surrounding knowledge manage-ment and organizational culture. Section 4 details our analysison optimal knowledge management strategies that cultivate theorganizational cultural fit, and maximize the organizationalprofit. Section 5 concludes the paper.

*Correspondence: Sajjad M Jasimuddin, Department of Strategy andEnvironment, Kedge Business School, Marseille Campus, Marseille, 13288,France.E-mail: [email protected]

Journal of the Operational Research Society (2013), 1–11 © 2013 Operational Research Society Ltd. All rights reserved. 0160-5682/13

www.palgrave-journals.com/jors/

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2. Knowledge categorization, strategy, andorganizational culture

This section reviews the relevant literature to identify the rootsof the dilemma between tacit and explicit knowledge. Itcontinues by cautioning against over-emphasizing one type ofknowledge, while neglecting the other, and prescribes a strategythat seems to encourage the use of both tacit knowledge andexplicit knowledge in complementary ways so as to enhance thecompetitive advantage of an organization.

2.1. Knowledge as a category

To date, it seems that two dominant types of knowledge haveemerged based on the dimension of tacitness: tacit and expli-cit knowledge. This categorization is embedded in the vastmajority of current literature on organizational knowledge (eg,Blackler, 1995; Nonaka and Takeuchi, 1995; Roberts, 2004),which suggests that tacit and explicit knowledge represent twoseparate types of knowledge having distinct features. Table 1demonstrates the salient features of tacit and explicit knowl-edge. Tacit knowledge, as first used by Polanyi (1967), isconstructed from individuals’ own experience in the world andalso forms the basis for explicit knowledge.Reflecting this view, several academics (eg, Connell et al,

2003; Roberts, 2004) argue that tacit knowledge is embodied inthe human brain, and cannot be separated from the people whopossess it, and thereby it is difficult to access and transfer. Incontrast, explicit knowledge can be codified, documented, andtransmitted, making it easily and cheaply available to a largenumber of people at a marginal cost (Roberts, 2004).

2.2. Strategies to handle tacit and explicit knowledge

Several researchers (eg, Hansen et al, 1999; Scheepers et al,2004; Jasimuddin and Zhang, 2009) suggest two very differentstrategies in order to manage knowledge: the personalizationstrategy and the codification strategy. The personalizationstrategy addresses the storage of tacit knowledge in humanminds and the transfer of such knowledge through face-to-faceinterface (Jasimuddin, forthcoming). On the other hand, thecodification strategy focuses on explicit knowledge, allowingknowledge to be easily articulated and stored in computer oran artefact so that relevant knowledge is easily available touse. Most specifically, Hansen et al (1999) argue that thepersonalization strategy is an approach where knowledge isclosely tied to the person who developed it and, is sharedwith others mainly through direct person-to-person inter-actions; and the codification strategy is another approachwhere knowledge can be accessed and used easily by anyonein an organization.However, academics agree that both the personalization and

codification strategies have negative and positive impacts(Table 2). Several authors, most notably Spender (1995),Alvesson (2001), Johannessen et al (2001), and Hall andAndriani (2003), identify the advantages of using tacit knowl-edge. Spender (1995), for example, contends that tacit knowl-edge held by an organization is the most secure and strategicallysignificant kind of knowledge since other organizations wouldfind it difficult to imitate. This view is an extension to that ofHall and Andriani (2003) who characterize it as ‘externallysafe’. Since tacit knowledge is ambiguous in nature, theambiguity makes duplication of the knowledge difficult (Halland Andriani, 2003). Moreover, other researchers identify thebenefits that a firm can gain from using tacit knowledge in termsof its contribution to innovation (Alvesson, 2001) and lowinvestment in information technologies (Johannessen et al,2001).On the other hand, explicit knowledge can be easily commu-

nicated and stored because such knowledge is codified. There islittle chance of losing explicit knowledge due to employeeturnover. The fact is that such knowledge is available inorganizational repositories, and is accessed to be used byanyone in the organization (Grant, 1996; Hansen et al, 1999).As a result, organizations are investing heavily in electronicsystems, hoping to increase their ability to manage the vastarray of explicit knowledge (Choi et al, 2010). Alternatively,the codifying knowledge can involve high expenditure and lead

Table 1 Salient features of tacit and explicit knowledge

Features Tacit knowledge Explicit knowledge

Content Non-codified CodifiedArticulation Difficult EasyLocation Human brains Computers, artifactsCommunication Difficult EasyMedia Face-to-face contact,

storytellingInformationtechnology

Storage Difficult EasyStrategy Personalization CodificationOwnership Organization and its

membersOrganization

Table 2 Positive and negative effects of knowledge strategies

Strategy Positive side Negative side

Personalization Low risk of imitation Low investment in IT Highrate of innovation Sense of ambiguity

Difficult to communicate Difficult to store Reluctant to share knowledgeNo protection through IPRs Knowledge loss due to labour turnover

Codification No knowledge loss due to labour turnover Protectionthrough IPRs Easy to communicate Easy to store

High investment in IT Large space to keep documents High risk ofimitation by competitors

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to excessive documentation (Boiral, 2002). Furthermore, themain difficulty in using explicit knowledge is that there is highrisk of imitation by rival organizations, leading to loss ofcompetitive advantage. In this regard, Hall and Andriani(2003) comment that explicit knowledge is ‘internally safe’,but ‘externally vulnerable’. However, it can be protectedthrough intellectual property rights (Antonelli, 1997).Since both personalization and codification strategies have

positive and negative implications, neither the personalizationstrategy nor the codification strategy alone is sufficient tomanage organizational knowledge. Hence the personalizationand codification approaches need to be integrated so that thebenefits of both tacit and explicit knowledge can be gained.Accordingly, an organization should seek an integratedapproach to knowledge management that ensures the contribu-tion of the strategies: a symbiosis strategy. Drawing on the workof Hansen et al (1999), others (eg, Scheepers et al, 2004;Jasimuddin and Zhang, 2009) make a case for a symbiosisstrategy in managing knowledge, stating that such anapproach to knowledge management helps maximize thebenefits of the personalization and codification approaches.A successful symbiosis strategy is one that takes advantageof the positive features of both strategies, reflecting anintegrated framework where an organization can practiceboth strategies simultaneously in a balanced manner. It canbe argued that the implementation of a symbiosis strategycan be realized in practice by developing an appropriateorganizational culture.Such a mixed strategy would be based upon an organiza-

tional culture, which is conducive to ease knowledge replicationwithin the organization but presents difficulty in imitation by itscompetitors. This culture needs to be strong and pervasivewithin the organization, but at the same time idiosyncraticand unique to the organization. The fact that an idiosyn-cratic organizational culture provides a language or code inwhich knowledge can be exchanged among members of anorganization who possess the cultural key. For subscribersto the culture, the exchange takes place in terms of explicitknowledge, because its tacit components are embeddedwithin the culture and are understood by its members. Tooutsiders, the knowledge that the insiders work withappears ‘sticky’ in nature (Szulanski, 1996), as they donot possess the cultural key to fully apply it as explicitknowledge.In this regard, Brown and Duguid (1991) describe the process

of learning within the context of a community of practice asone in which learners ‘acquire that particularly commu-nity’s subjective viewpoint and learn to speak its language… they are enculturated … acquiring … the embodiedability to behave as community members’ (p 48). Thisenculturation provides a context in which members of thecommunity can exchange knowledge about practice, in amanner that is comparatively difficult to comprehend byoutsiders, apparently relying on a great deal of tacitness, butis fairly explicit to insiders.

3. The model of knowledge management andorganizational culture

Organizational culture is regarded as a critical success factor forimplementing knowledge management (De Long and Fahey,2000; Janz and Prasarnphanich, 2003; King, 2007). A con-ducive organizational culture fosters the sharing of the existingknowledge and creating new knowledge and capabilities (Alaviet al, 2005). Cultural fit is employed to model the congruence ofworkers within a given organizational culture. On the basis ofthe definition of cultural fit and its analytical framework fromprior research (Carrillo and Gromb, 1999), we further develop aknowledge management model that can improve a firm’scultural fit. Thus, firms seek to have the best knowledgemanagement strategy so as to leverage tacit and explicit knowl-edge within an organization that seems to increase cultural fit,and maximize organizational profit. The specific setting of ourmodel unfolds as follows.A firm hires knowledge workers (measured at 1) from a

labour market to perform a series of tasks for infinite periods.From the labour market, only ϕ proportion of the hired workershave the necessary knowledge K, ‘fit’ for the organizationalculture A, to perform their tasks. In each period, workersgenerate a revenue RL when they are not fit for the culture Aand RH=RL+Δ otherwise. Workers get a fixed wage paymentw in each period, no matter whether they are fit or not for theculture A. Assume that the revenue generated from each workeris always greater than the wage payment, that is, RL>w. At theend of each period, a worker quits the firm with the probability1− λ and joins other firm to perform the same task under adifferent culture B. In addition, the firm screens workers at theend of each period to check whether workers are ‘good fits’ forcurrent culture A. Those who do not have the knowledge K willbe identified and fired with probability p. The left and firedworkforce will be replenished from the labour market.In a firm with the current established culture A, the knowl-

edge K possessed by a worker is perceived as explicit withprobability σ and tacit with probability 1− σ. The PerceivedExplicitness of Knowledge (PEK) within an organization can betraced back from the study by Polanyi (1967), where knowl-edge is perceived as an integral object with both explicit andtacit components. The concept of PEK (σ) is one of the linkagesbetween knowledge management and organizational culturein order to study the impact of organizational culture fiton knowledge management. Table 3 depicts a summary of thenotation used in the paper.On the basis of the combined explicit and tacit nature of

knowledge K, a firm applies knowledge management strategy(ie, personalization or codification) to facilitate knowledgesharing and learning among hired workers in each period sothat the unfit workers may become fit after learning to acquireknowledge K. While implementing different knowledge man-agement strategies, the firm takes into account the followingmajor tradeoffs between these two strategies (as shown inTable 2): (a) loss of knowledge due to labour turnover, (b) IT

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investment, (c) imitation by competitors, (d) codification andstorage of knowledge, and (e) ease to communicate.When the knowledge transfer initiatives are implemented in

time period t, ρt proportion of initially unfit workers willbecome fit for the culture A. The other 1− ρt proportion remainsunfit with the culture A. The proportion ρt, the KnowledgeManagement Performance Quotient (KMPQ) in the timeperiod t, measures the effect of knowledge managementstrategies on organizational culture fit, that is, the proportion ofculturally unfit workers that has been transformed into fit onesgiven the effort exerted by the firm in promoting knowledgetransfer within the firm. In general, the firm has to incur morecosts when exerting more efforts in implementing either thepersonalization or codification strategy. The knowledge man-agement investment (ie, cost) in the time period t is V(σ, ρt).Contingent on the perceived explicitness (σ) of knowledgewithin an organization, the firm adopts both knowledge man-agement strategies—personalization and codification. In thisregard, the knowledge management investment function isdefined as V(δ, ρt)= [σCe(ρt) + (1− σ)Ca(ρt)]K, where Ce(ρt)and Ca(ρt) are the costs for knowledge management implemen-tation in explicit and tacit knowledge, respectively, and bothcosts convexly increase in the KMPQ ρt. For convenience ofrepresentation and ease of tractability, we assume that Ce(ρt)=θeρt

2/2 and Ca(ρt)= θaρt2/2, where θe and θa are the unit costs to

implement knowledge management strategies, representing thedifficulties in transferring explicit and tacit knowledge,respectively.In summary, Figure 1 captures the main features of our

model. Cultural fit is employed to describe organizationalculture, and the performance of knowledge management strate-gies can be measured by KMPQ. In addition, knowledgemanagement strategies influence organizational culture by

improving cultural fit, and organizational culture impactsknowledge management initiatives through enhancing thePEK. When the organizational cultural fit increases, moreworkers will possess knowledge K, which enables them toarticulate more about the tacit part of the knowledge. Hence, thePEK increases with the cultural fit. Given the formulation aboutknowledge management and organizational culture, in the firstperiod, the firm’s organizational cultural fit is

ϕ1 ¼ ½ϕ + ð1 -ϕÞρ1�λ+ fð1 -ϕÞð1 - ρ1Þð1 - λÞ + ð1 -ϕÞð1 - ρ1Þλp+ ½ϕ + ð1 -ϕÞρ1�ð1 - λÞgϕ>ϕ;

where the term [ϕ+ (1−ϕ)ρ1]λ stands for the culturally fitworkers who decide to stay, including those that have beentransformed from culturally unfit into fit ones, the term (1−ϕ)(1− ρ1)(1− λ) denotes the workers who remain unfit andeventually quit the firm, the term (1−ϕ)(1− ρ1)λp representsthe workers who remain unfit and want to stay, but are firedbecause they are identified as culturally unfit, and the last term[ϕ+ (1−ϕ)ρ1](1− λ) corresponds to the culturally fit workerswho quit the firm. Those workers who quit the firm, eithervoluntarily or being fired, will be replenished from the labourmarket with the probability ϕ of being culturally fit with thecurrent culture A.Generally, the firm’s cultural fit ϕt in time period t can be

expressed with a function of the cultural fit ϕt− 1 in time periodt− 1 as

ϕt ¼ ½ϕt - 1 + ð1 -ϕt - 1Þρt�λ+ fð1 -ϕt - 1Þð1 - ρtÞð1 - λÞ + ð1 -ϕt - 1Þð1 - ρtÞλp+ ½ϕt - 1 + ð1 -ϕt - 1Þρt�ð1 - λÞgϕ

¼ λð1 - ρtÞð1 - pϕÞϕt - 1 + ½1 - λ + λpð1 - ρtÞ�ϕ + λρt:

By examining the relationship between the cultural fit andKMPQ in the same period, we can infer that the cultural fit canalways be improved by increasing the KMPQ because thederivative of the cultural fit with respect to the KMPQ in eachperiod is always positive, that is,

∂ϕt

∂ρt¼ λð1 -ϕt - 1Þð1 - pϕÞ>0:

Table 3 Summary of notation

A current organizational culture in firm XB organizational culture in the competing firm Yβ discount rateCe total cost of achieving KMPQ ρt for explicit knowledge in time

period tCa total cost of achieving KMPQ ρt for tacit knowledge in time

period tΔ difference of revenues between culturally fit and unfit workersλ probability of a worker staying in the firm in each periodp probability of a worker being identified as unfit in each periodϕ probability of a worker having knowledge K on the marketϕt organizational cultural fit in time period tRL revenue from culturally unfit workersRH revenue from culturally fit workersρt knowledge management performance quotient (KMPQ) in time

period tσ perceived explicitness of knowledge (PEK) within the firmt index for time periodsθe unit cost for explicit knowledgeθa unit cost for tacit knowledgew fixed wage payment for workers in each period

Figure 1 Relationship between knowledge management andorganizational culture.

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Accordingly, the firm’s total payoff at the end of timeperiod t is

πt ¼Xt

i¼1

βi - 1fðRL -wÞ +ϕiΔ - ½σCeðρtÞ + ð1 - σÞCtðρtÞ�Kg;

which is a concave function of ρt. Hence, the firm’s decisionproblem is to determine how to implement knowledge manage-ment strategies to achieve the best KMPQ in each period toshape its organizational culture, maximizing its total profit. Wenext show the firm’s optimal decision for its knowledgemanagement practices under different scenarios. All proofs canbe found in the Appendix.

4. Optimal knowledge management practices

We analyse the firm’s optimal knowledge management prac-tices in each period to increase its organizational cultural fit, andthereby achieve a maximal profit. Beginning with the investiga-tion of the one-period best KMPQ, we then analyse the optimalknowledge management practices in two cases, achieving eitherthe homogeneous or heterogeneous KMPQ in each period. Inaddition, we study the impact of the cultural fit on the firm’sknowledge management practice through the changeable PEKin each period. Finally, we explore the optimal knowledgemanagement practice under competition.

4.1. One-period KM practice

We first investigate the best KMPQ in a single period, whichprovides valuable insights for the further analysis of dynamicsettings. To choose a best KMPQ for its PEK σ, the firm has toincur a certain amount of knowledge management cost V(σ, ρ1).For the same amount of such cost, the substitution rate betweenthe PEK σ and KMPQ ρ1 is

dρ1dσ

¼ -∂Vðσ;ρ1Þ

∂σ∂Vðσ;ρ1Þ

∂ρ1

¼ -Ceðρ1Þ -Caðρ1Þ

σC0eðρ1Þ + ð1 - σÞC0

aðρ1Þ;

which implies that the iso-cost curves can be either increasingor decreasing.

Figure 2 demonstrates the firm’s iso-cost and iso-revenuecurves in both cases. The firm’s revenue is RL−w+ϕΔ, whereϕ1= λ(1− ρ1)(1− pϕ)ϕ+ [1− λ+ λp(1− ρ1)]ϕ+ λρ1. Since therevenue is linearly increasing in the KMPQ ρ1, the maximalrevenue is achieved at ρ1= 1. However, with this KMPQ, thefirm has to incur huge knowledge management investmentV(σ, 1), which leads to a low profit. Therefore, the firm has tofind an optimal KMPQ ρ*, which requires a lower knowledgemanagement investment but the revenue does not drop toomuch, generating a maximal profit.When it is expensive to transfer tacit knowledge, the firm’s

optimal profit increases in the PEK. In contrast, when it iscostly to transfer explicit knowledge, the firm’s optimal profitdecreases in the PEK. This changing pattern of the firm’s profitwith respect to PEK is intuitive. As shown in Figure 2, when itis more expensive to transfer tacit knowledge, the firm willincur a lower KM cost for the same KMPQ ρ* and a higherPEK σ′ (PEK increases from σ to σ′), leading to a higher profit.In a similar vein, when it is more costly to transfer explicitknowledge, the firm will incur a lower KM cost for the sameKMPQ ρ* and a lower PEK σ′ (PEK decreases from σ to σ′),resulting in a higher profit.

4.2. Homogeneous KMPQ

In this subsection, we assume that the firm wants to implementknowledge management practices such that the KMPQ isconsistent in each period, that is, ρi= ρ, ∀ i= 1, 2,…,∞. Wenext show that there exists such a homogeneous KMPQ for aninfinite horizon to maximize the firm’s total profit, and thendiscuss some features of the optimal homogeneous KMPQ.

Proposition 1 There exists a homogeneous KMPQ ρi= ρ,∀ i= 1, 2,…,∞, to maximize the firm’s total profit, andimprove cultural fit over time.

Proposition 1 demonstrates that the firm’s cultural fit will beimproved by implementing the best homogenous KMPQ, andthe firm’s overall profit will be maximized as well. The optimalhomogeneous KMPQ changes with the parameters λ, ϕ, and P,which is summarized in the following proposition.

Figure 2 Iso-profit and iso-cost curves: (a) Cheaper to transfer explicit knowledge; (b) Cheaper to transfer tacit knowledge.

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Proposition 2 The firm should invest more on knowledgemanagement to achieve an optimal homogeneous KMPQ,when (1) the probability of workers having knowledge Kon the market drops (ϕ decreases); (2) it is more difficult toscreen workers’ cultural fits (P decreases); and (3) lessworkers quit the company in each period (λ increases).

Proposition 2 is intuitive. When fewer workers on the marketpossess knowledge K, the firm has to increase its knowledgemanagement investment to obtain a higher optimal KMPQ sothat more workers will be able to acquire knowledge K throughthe firm’s initiatives on knowledge management. Similarly,when it is very difficult to identify unfit workers or fewerworkers quit their jobs, there is a possibility that more culturallyunfit workers will be residing in the firm. Therefore, the firmhas to increase its optimal KMPQ as well to transform moreworkers into being culturally fit. Next, we study the effects ofPEK σ and costs on the optimal homogeneous KMPQ ρ andsummarize the results in the following proposition.

Proposition 3 In an organizational culture where tacitknowledge is easier to be transferred than explicit knowl-edge, when the degree of tacitness of knowledge increasesfor knowledge, a firm should exert more effort in promot-ing knowledge transfer among workers. In contrast, in anorganizational culture where explicit knowledge is easierto be transferred than tacit knowledge, when the degree ofexplicitness of knowledge increases for knowledge, a firmshould exert more effort in promoting knowledge transferamong workers.

Table 4 summarizes the effects of PEK and cost changes onthe KMPQ. When the PEK increases within the organization,the firm may try to increase, decrease, or remain its KMPQ,contingent on the unit cost of knowledge management practicesfor explicit and tacit knowledge. When it is more expensive totransfer tacit than explicit knowledge, the firm should increaseits KMPQ if the PEK increases. In a similar situation, when it isless costly to transfer tacit than explicit knowledge (which israre in practice), the firm should increase its KMPQ if the PEKdecreases. Otherwise, the firm is better off by keeping orlowering its KMPQ for the current period. The result fromProposition 3 is consistent with that in the single-period setting.

4.3. Heterogeneous KMPQ

Instead of supporting a homogeneous KMPQ, the firm mayintend to maximize its total profit without maintaining theconsistency of KMPQs in each time period. We first investigate

the firm’s problem for a finite time horizon, which leads into thesolution to the infinite time horizon, and then analyse how thecultural fit and the best KMPQ change in an infinite timehorizon.

Proposition 4 The optimal heterogeneous KMPQ over n timeperiods can be characterized as follows,

ρn - t ¼ τð1 -ϕn - t - 1Þ + τβtλtð1 - pϕÞtð1 -ϕn- t - 1ÞYn

i¼n - t + 1

ð1 - ρiÞ;

ρn ¼ τð1 -ϕn - 1Þ; 8t ¼ 1; 2; ¼ ; n - 1;

where

τ ¼ λð1 - pϕÞΔK½σθe + ð1 - σÞθa� :

Following Proposition 4, we derive the next corollary tofurther describe the relationship of the heterogeneous KMPQwith the firm’s organizational cultural fit in a long run.

Corollary 5 As n goes to infinity, the KMPQ in each period tis, ρt= τ(1−ϕt− 1), ∀ t= 1, 2,…,∞ and ϕ0=ϕ.

In Proposition 4, the term τ is essentially the optimal KMPQin a single period when the initial organizational cultural fit iszero. Therefore, τ describes the best KMPQ to transformculturally unfit workers into fit ones by implementing knowl-edge management initiatives in a single period when all theworkers are culturally unfit. In this regard, we formally define τas the Primary Knowledge Management Performance Quotient(Primary KMPQ). Consequently, Corollary 5 follows Proposi-tion 5 to show that the optimal KMPQ in each period is theproduct of the Primary KMPQ with the organizational culturalfit in the previous period, which demonstrates the intuitive anddirect relationship between KMPQ and organizational culturalfit. Next, we discuss the properties of the organizational culturalfit and the heterogeneous KMPQ in the long run in thefollowing proposition.

Proposition 6 Under the sufficient condition that τ⩽ 1/2, thecultural fit ϕt concavely increases and the optimal KMPQρt convexly decreases, for all t= 1, 2,…,∞.

Proposition 6 implies that when the Primary KMPQ is not solarge such that the firm only has to transform less than half of allthe workers into being culturally fit, the organizational culturalfit will keep increasing with a decreasing KMPQ in each periodin the long run. This intuition can be inferred because undersuch condition, the difference of the organizational cultural fitbetween two consecutive periods always decreases with thetime. Finally, other parameters including the quitting rate 1− λand screening rate p have the same effect on the Primary KMPQand the KMPQ in each period as that in the homogeneous case.

4.4. Changeable PEK

Previous subsections only study the one-way relationship fromknowledge management to organizational culture by assuming

Table 4 Effects of PEK and cost changes on KMPQ

Costs PEK σ increases PEK σ decreases

θe> θa KMPQ ↓ KMPQ ↑θe= θa no effect on KMPQθe< θa KMPQ ↑ KMPQ ↓

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the PEK is not changeable. However, as our model settingdemonstrates in Figure 1, the firm’s cultural fit also influencesits knowledge management practice by improving the PEK. Inthis subsection, we explore the effect of the firm’s cultural fit onits knowledge management performance.In reality, the PEKmay not be constant in each period. When

the organizational cultural fit increases, more workers willbecome the possessors of knowledge K; therefore, they tend toarticulate more about the tacit part of the knowledge. Hence, thePEK will increase with the cultural fit. In this respect, weconsider that σ also changes in each period and the PEK σt intime period t depends on the cultural fit ϕt− 1 in the previousperiod. The following proposition shows how the best KMPQchanges with the firm’s cultural fit under different conditions foran infinite time horizon.

Proposition 7 When it is less expensive to transfer tacitknowledge, or θe> θa, ρt decreases in ϕt− 1; in contrast,when it is less expensive to transfer explicit knowledge, orθe< θa, ρt first increases and then decreases in ρt− 1 at thethreshold cultural fit level

ϕt - 1⩽σðθa - θeÞ

σðθa - θeÞ + θa :

When it is less expensive to transfer tacit knowledge, knowl-edge management initiatives will become less expensivebecause the tacitness of knowledge decreases when the timegoes on. In contrast, when it is less costly to transfer explicitknowledge, knowledge management initiatives will be lessexpensive as well because the PEK increases in each timeperiod with the organizational culture fit. Therefore, the firmwill increase its KMPQ in each time period until its cultural fitreaches certain threshold ϕt - 1. Beyond this threshold, the PEKcannot be increased anymore and will reach its limit σ, so thefirm’s KMPQ will begin to decrease.Our model assumes that a knowledge management invest-

ment is a function of both the firm’s PEK and KMPQ, so thethreshold cultural fit ϕt - 1 is related to the maximal PEK σ thatcan be reached and the unit costs of transferring explicit andtacit knowledge. When the difference between knowledgetransfer costs increases, the threshold cultural fit also increases.

4.5. Optimal KMPQ under competition

Having investigated the optimal KMPQ within a firm, we nextanalyse the firm X’s optimal KMPQ under the competition fromfirm Y. To investigate the influence of the firm X’s knowledgemanagement practice on its competitor, we isolate its effect byassuming that firms X and Y are only related by the labourmarket. Both X and Y apply the knowledge K in theirproductions and replenish their workforce with the knowledgeK from the same labour market in each time period. However,Kis perceived as explicit with probability δ and 1− δ as tacitwithin the competing organization for its culture B. Those who

quit from firm X will never come back again, and may join firmY and vice versa.To simplify the analysis without sacrificing meaningful

insights, we consider a two-period model for both firms X andY. Our prior analysis shows that [ϕ+ (1−ϕ)ρ1

X](1− λX) propor-tion of workers1 who are culturally fit with culture A in firm Xwith the knowledge K will quit firm X at the end of the firstperiod. Suppose they will not return to firm X again, then theproportion of workers on the market with the knowledge K forfirm Y will increase to be

ϕY ¼ ϕ + ½ϕ + ð1 -ϕÞρX1 �ð1 - λXÞ1 + ½ϕ + ð1 -ϕÞρX1 �ð1 - λXÞ

:

Similarly, the workers who quit from firm Y in the first periodwill increase this proportion for firm X to be

ϕX ¼ ϕ + ½ϕ + ð1 -ϕÞρY1 �ð1 - λYÞ1 + ½ϕ + ð1 -ϕÞρY1 �ð1 - λYÞ

:

Therefore, firm X’s total payoff in two periods can beformulated accordingly with the method shown in Appendix Dand the optimal KMPG ρ2

X for firm X in the second period canbe solved as

ρX2 ¼ λð1 -ϕ1Þð1 - pϕXÞΔK½σθe + ð1 - σÞθa� :

Since ϕX is always greater than ϕ and the PEK remains thesame, ρ2

X is less than that without the competition and firm X’sprofit increases accordingly. Reciprocally, for firm Y, theoptimal KMPG ρ2

Y in the second period is also less than thatwithout the competition and its profit increases as well. Becauseof the quitting workers from their competitor in the first periodcan use the same knowledge in the other firm to its full capacity,the firms will have a better chance of replenishing their work-forces with the knowledge K in the second period. In thisregard, they will incur a lower cost for improving theirorganizational cultural fit with knowledge management prac-tices. This rationale clearly demonstrates a strategy that thefirms should use to inhibit their quitting workers from using thesame knowledge in a different culture. The strategy needs toestablish an organizational culture for workers to adeptly usetheir knowledge K within a firm, but to make it ‘sticky’ if theyattempt to quit the firm and use the knowledge in a differentculture. Although workers may use various ways to facilitatethe transformation of knowledge between its tacit and explicitcomponents (Nonaka, 1994; Stover, 2004; Nonaka et al, 2013)to overcome its ‘stickiness’, it is never an easy task within ashort period of time, which is worth analysis in future studies toinvestigate firms’ best strategies of knowledge transformationunder competition.

1The superscript differentiates firm X from firm Y, applicable for all thenotations.

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5. Conclusion

Knowledge management has received much attention in describ-ing the ways of how tacit and explicit knowledge are conceptua-lized. This paper firmly addresses the strategies of knowledgemanagement, suggesting the development of a mixed strategy tocreate an environment that eases knowledge replication withinthe organization but at the same time makes it difficult for itscompetitors to imitate. The protective nature of the culture weenvisage would be reinforced so as to encourage the transfer oftacit knowledge among themselves, and at the same timediscourage the transfer of their knowledge to outsiders.Our analytical study begins with the optimal knowledge

symbosis strategy for a firm without competition. A firm caneither maintain a homogeneous or heterogeneous KMPQ ineach period to increase its cultural fit, maximizing its long-termprofit. We then turn to the investigation of knowledge manage-ment strategy under competition. Our analysis shows that a firmshould try to either retain workers fit with the current culture ordevelop a culture such that workers with knowledge K are onlyproductive under the current culture. In other words, if the firmcannot control the quitting rate, it should protect the benefits ofits knowledge from flowing into its competitor. One method ofsuch protection is to ensure that the PEK is high within the firmbut low outside the firm, when it is less expensive to transferexplicit knowledge. If we assume that the productivity level isrelated to the PEK of knowledge K within the firm, then theworkers quitting from firm X with a high PEK will not be asproductive as they work in a different culture. Therefore,everything else being equivalent between firms X and Y,whichever adapt its organizational culture to achieve a higherPEK will gain a competitive edge.This paper provides valuable insights for managers to under-

stand the fundamental relationship between knowledge man-agement and organizational culture, and also presents practicalguidance to adopt appropriate knowledge management strategy.However, it should be noted that our analytical results are basedon some specific assumptions, and may not be directly appliedin real scenarios. For instance, we assume that tacit knowledgecannot be converted into explicit, and workers all have the samePEK in the same period. Future extensions may relax theseassumptions, and further the analysis by focusing on thedifference between explicit and tacit knowledge and studyingits effects on the optimal strategy. Another important issue thatmight be interested to a wider operational research-orientedaudience is knowledge type transformation, and the realistictime span for doing and observing such knowledge transforma-tion. Since this has not been addressed in this paper, futureresearch may integrate the transformation of knowledge typesin the framework of organizational culture, and investigate itseffect on knowledge management strategies.

Acknowledgements—The paper has benefitted from the valuable commentsof two anonymous referees and the helpful inputs from the Editors. Wewould like to thank them.

References

Alavi M, Kayworth TR and Leidner DE (2005). An empirical examinationof the influence of organizational culture on knowledge managementpractices. Journal of Management Information Systems 22(3): 191–224.

Alvesson M (2001). Knowledge work: Ambiguity, image and identity.Human Relations 54(7): 863–896.

Antonelli C (1997). New information technology and the knowledge-based economy: The Italian evidence. Review of Industrial Organiza-tion 12(4): 593–607.

Blackler F (1995). Knowledge, knowledge work and organizations: Anoverview and interpretation. Organization Studies 16(6): 1021–1046.

Boiral O (2002). Tacit knowledge and environmental management. LongRange Planning 35(3): 291–317.

Brown J and Duguid P (1991). Organizational learning and communitiesof practice: Toward a unified view of working, learning, and innova-tion. Organization Science 2(1): 40–57.

Carrillo JD and Gromb D (1999). On the strength of corporate cultures.European Economic Review 43(4–6): 1021–1037.

Choi SY, Lee H and Yoo Y (2010). The impact of informationtechnology and transactive memory systems on knowledge sharing,application, and team performance: A field study. MIS Quarterly34(4): 855–870.

Connell NAD, Klein JH and Powell PL (2003). It’s tacit knowledge butnot as we know it: Redirecting the search for knowledge. Journal ofOperational Research Society 54(2): 140–152.

De Long DW and Fahey L (2000). Diagnosing cultural barriers to knowl-edge management. Academy of Management Executive 14(4): 113–127.

Drucker PF (1992). The new society of organizations. Harvard BusinessReview 70(5): 95–104.

Drucker PF (2000). Post-capitalist Society. Harper Collins: New York.Grant RM (1996). Toward a knowledge based theory of the firm.

Strategic Management Journal 17(Special Issue 1): 109–122.Hall R and Andriani P (2003). Managing knowledge associated with

innovation. Journal of Business Research 56(2): 145–152.Hansen TM, Nohria N and Tierney T (1999). What’s your strategy

for managing knowledge? Harvard Business Review 77(2): 106–116.Janz BD and Prasarnphanich P (2003). Understanding the antecedents of

effective knowledge management: The importance of a knowledge-centered culture. Decision Sciences 34(2): 351–384.

Jasimuddin SM (forthcoming). Face-to-face interface in software devel-opment: Empirical evidence from a geographically dispersed high-tech laboratory. International Journal of Technology and HumanInteraction 10(1): accepted.

Jasimuddin SM and Zhang Z (2009). The symbiosis mechanism foreffective knowledge transfer. Journal of the Operational ResearchSociety 60(5): 706–716.

Jasimuddin SM and Zhang Z (2011). Transferring stored knowledge andstoring transferred knowledge. Information Systems Management28(1): 84–94.

Jasimuddin SM, Klein JH and Connell C (2005). The paradox of usingtacit and explicit knowledge: Strategies to face dilemmas. Manage-ment Decision 43(1): 102–112.

Jasimuddin SM, Connell C and Klein JH (2012). Knowledge transferframeworks: An extension incorporating knowledge repositories andknowledge administration. Information Systems Journal 22(3): 195–209.

Johannessen J, Olaisen J and Olsen B (2001). Mismanagement of tacitknowledge: The importance of tacit knowledge, the danger ofinformation technology, and what to do about it. InternationalJournal of Information Management 21(1): 3–20.

King WR (2007). A research agenda for the relationships betweenculture and knowledge management. Knowledge and Process Man-agement 14(3): 226–236.

Klein J, Connell C and Jasimuddin M (2007). Who needs memory?The case for the Markovian organisation. Knowledge ManagementResearch & Practice 5(2): 110–116.

8 Journal of the Operational Research Society

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Miller DJ, Fern MJ, and Cardinal LB (2007). The use of knowledge fortechnological innovation within diversified firms. Academy of Man-agement Journal 50(2): 308–336.

Nonaka I (1994). A dynamic theory of organizational knowledgecreation. Organization Science 5(1): 14–37.

Nonaka I and Takeuchi H (1995). The Knowledge Creating Company.Oxford University Press: Oxford, UK.

Nonaka I, Kodamab M, Hirosec A and Kohlbacherd F (2013). Dynamicfractal organizations for promoting knowledge-based transformation –A new paradigm for organizational theory, European ManagementJournal, available online publication, 22 March, http://dx.doi.org/10.1016/j.emj.2013.02.003.

Polanyi M (1967). The Tacit Dimension. Routledge & Kegan Paul Ltd:London.

Quinn JB, Anderson P and Finkelstein S (2004). Leveraging intellect.Academy of Management Executives 10(3): 7–27.

Roberts J (2004). From know-how to show-how? Questioning the role ofinformation and communication technologies in knowledge transfer.Technology Analysis and Strategy Management 12(4): 429–443.

Scheepers R, Venkitachalam K and Gibbs MR (2004). Knowledgestrategy in organizations: Refining the model of Hansen, Nohria andTierney. Journal of Strategic Information Systems 13(3): 201–222.

Spender JC (1995). Organizational knowledge, collective practice andPenrose rents. International Business Review 3(4): 1–5.

Stover M (2004). Making tacit knowledge explicit: The Ready ReferenceDatabase as codified knowledge. Reference Services Review 32(2):164–173.

Szulanski G (1996). Exploring internal stickiness: Impediments to thetransfer of best practice within the firm. Strategic ManagementJournal 17(Winter Special Issue 1): 24–43.

Walsh JP and Ungson GR (1991). Organizational memory. Academy ofManagement Review 16(1): 57–91.

Appendix

A. Proof of proposition 1

Proof The generic term of the cultural fit at time period t canbe obtained as

ϕt ¼½1 - λ + λpð1 - ρÞ�ϕ + λρ1 - λð1 - ρÞð1 - pϕÞ

- λtð1 - ρÞtð1 - pϕÞt λϕ½pð1 - ρÞð1 -ϕÞ + ρ� + λρ1 - λð1 - ρÞð1 - pϕÞ :

Since ∂ϕt/∂t> 0, the cultural fit increases over time. In thelong run, the cultural fit is

ϕ1 ¼ ½1 - λ + λpð1 - ρÞ�ϕ + λρ1 - λð1 - ρÞð1 - pϕÞ ;

whose derivative with respect to ρ is

∂ϕ1∂ρ

¼ λð1 - λÞð1 -ϕÞð1 - pϕÞ½1 - λð1 - ρÞð1 - pϕÞ�2 >0:

At the end of time period t, the firm’s total payoff is

πt ¼Xt

i¼1

βi - 1fðRL -wÞ +ϕiΔ - ½σCe + ð1 - σÞCt�Kg:

In the long run, the firm’s total payoff is

π1 ¼ ðRL -wÞ1 - β

-½σCe + ð1 - σÞCt�K

1 - β

+½1 - λ + λpð1 - ρÞ�ϕ + λρ

½1 - λð1 - ρÞð1 - pϕÞ�ð1 - βÞΔ;

and its first order condition with respect to ρ yields that

λð1 - λÞð1 -ϕÞð1 - pϕÞ½1 - λð1 - ρÞð1 - pϕÞ�2 Δ ¼ ρK½σθe + ð1 - σÞθa�; (A.1)

whose LHS decreases and RHS increases in ρ. Therefore, thereexists an optimal homogeneous ρ* that can be implemented bythe firm in the infinite time horizon. □

B. Proof of proposition 2

Proof We define the LHS of Equation (A.1) as f(ρ, λ, p, ϕ).Hence, when f(ρ, λ, p, ϕ) increases(decrease) for the sameρ, the optimal KMPQ will increase(decrease) as well.In addition, it can be shown that ∂f (ρ, λ, p, ϕ)/∂ϕ< 0,∂f (ρ, λ, p,ϕ)/∂p< 0, and ∂f (ρ, λ, p, ϕ)/∂p< 0. □

C. Proof of proposition 3

Proof This can be shown from inspecting Equation (A.1).When θe> θa, ρ decreases in σ, so Ce(ρ) and Ca(ρ)increases when σ decreases. Similarly, when θe< θa, ρincreases in σ, so Ce(ρ) and Ca(ρ) increase when σincreases. □

D. Proof of proposition 4

Proof The firm’s payoff in each time period is

π1 ¼ ðRL -wÞ +ϕ1Δ - ½σCeðρ1Þ + ð1 - σÞCaðρ1Þ�K¼ ðRL -wÞ + fλð1 - ρ1Þð1 - pϕÞϕ+ ½1 - λ + λpð1 - ρ1Þ�ϕ + λρ1gΔ- ½σCeðρ1Þ + ð1 - σÞCaðρ1Þ�K;

π2 ¼ βfðRL -wÞ +ϕ2Δ - ½σCeðρ2Þ + ð1 - σÞCaðρ2Þ�Kg¼ βðRL -wÞ + βfλð1 - ρ2Þð1 - pϕÞϕ1

+ ½1 - λ + λpð1 - ρ2Þ�ϕ + λρ2gΔ- β½σCeðρ2Þ + ð1 - σÞCaðρ2Þ�K;

� � � � � �

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πt ¼ βt - 1fðRL -wÞ +ϕtΔ - ½σCeðρtÞ + ð1 - σÞCaðρtÞ�Kg

¼ βt - 1ðRL -wÞ + βt - 1fλð1 - ρtÞð1 - pϕÞϕt - 1

+ ½1 - λ + λpð1 - ρtÞ�ϕ + λρtgΔ

- βt - 1½σCeðρtÞ + ð1 - σÞCaðρtÞ�K;� � � � � �

πn ¼ βn - 1fðRL -wÞ +ϕnΔ - ½σCeðρnÞ + ð1 - σÞCaðρnÞ�Kg

¼ βn - 1ðRL -wÞ + βn - 1fλð1 - ρnÞð1 - pϕÞϕn- 1

+ ½1 - λ + λpð1 - ρnÞ�ϕ + λρngΔ

- βn - 1½σCeðρnÞ + ð1 - σÞCaðρnÞ�K;

where

ϕt ¼ λð1 - ρtÞð1 - pϕÞϕt - 1 + ½1 - λ + λpð1 - ρtÞ�ϕ + λρt:

The first order condition of ∑i= 1n πi with respect to ρn

indicates that

ρn ¼λð1 -ϕn - 1Þð1 - pϕÞΔK½σθe + ð1 - σÞθa� :

By using backward induction, the first order condition of∑i= 1

n πi with respect to ρn− 1 indicates that

λð1 -ϕn - 2Þð1 - pϕÞΔ -K½σθe + ð1 - σÞθa�ρn - 1+ βλ2ð1 - ρnÞð1 - pϕÞ2ð1 -ϕn - 2Þ ¼ 0:

Therefore,

ρn - 1 ¼λð1 -ϕn - 2Þð1 - pϕÞK½σθe + ð1 - σÞθa� Δ

+λ2ð1 - ρnÞð1 - pϕÞ2ð1 -ϕn - 2Þ

K½σθe + ð1 - σÞθa� βΔ: ðA:2Þ

In general,

ρn- t ¼λð1 -ϕn - t - 1Þð1 - pϕÞK½σθe + ð1 - σÞθa� Δ

+λt + 1ð1 - pϕÞt + 1ð1 -ϕn - t - 1Þ

Qni¼n - t + 1 ð1 - ρiÞ

K½σθe + ð1 - σÞθa� βt - 1Δ:ere

E. Proof of corollary 5

Proof The second term of Equation (A.2) is reduced to zerowhen n goes to infinity. □

F. Proof of proposition 6

Proof Since ρt= τ(1−ϕt− 1),

ϕt ¼ λð1 - ρtÞð1 - pϕÞϕt - 1 + ½1 - λ + λpð1 - ρtÞ�ϕ + λρt

¼ λð1 - pϕÞ½τð1 -ϕt - 1Þ2 +ϕt - 1� + ð1 - λ + λpÞϕ;

which implies that

ϕt -ϕt - 1 ¼ λð1 - pϕÞ½τð1 -ϕt - 1Þ2 - τð1 -ϕt - 2Þ2 +ϕt - 1 -ϕt - 2�¼ λð1 - pϕÞðϕt - 1 -ϕt - 2Þ½1 - 2τ + τðϕt - 1 +ϕt - 2Þ�:

Because ϕ1>ϕ, we know that ϕt−ϕt− 1> 0 as long as1− 2τ⩾ 0. In addition, the above equation suggests that thedifference of organizational cultural fit between two consecu-tive periods is decreasing with time. When ϕt increases, ρtalways decreases and the difference of KMPQ between twoconsecutive periods also decreases. □

G. Proof of proposition 7

Proof. At the end of time period t, the firm’s total payoff is

πt ¼Xt

i¼1

βi - 1fðRL -wÞ +ϕiΔ

- ½σiðϕi - 1ÞCeðρiÞ + ð1 - σtðϕi - 1ÞÞCtðρiÞ�Kg;

whose optimal KMPQ at time period t ρt over infinity timehorizon is,

ρt ¼λð1 -ϕt - 1Þð1 - pϕÞΔ

K½σtðϕt - 1Þθe + ð1 - σtðϕt - 1ÞÞθa�:

The above equation implies that strong cultural fit may alsorequire the firm to invest more in KM if

Hðϕt - 1Þ ¼1 -ϕt - 1

σtðϕt - 1Þθe + ð1 - σtðϕt - 1ÞÞθa

increases in ϕt− 1. When θe> θa, H(ϕt− 1) always decreasesin ϕt− 1. When θe>θa, H(ϕt−1), the first order derivative ofH(ϕt− 1) with respect to ϕt− 1 is

∂Hðϕt - 1Þ∂ϕt - 1

¼ - ½ð1 -ϕt - 1Þ∂σt

∂ϕt - 1+ σtðϕt - 1Þ�ðθe - θaÞ - θa⩾0;

if

ð1 -ϕt - 1Þ∂σt

∂ϕt - 1+ σtðϕt - 1Þ⩾

θaθa - θe

;

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which, being solved as a differential equation2, impliesthat,

σtðϕt - 1Þ⩾ϕt - 1

1 -ϕt - 1� θaθa - θe

; :

Suppose that the PEK K can only be increased to themaximal level as σ, then

σ ⩾ ϕt - 1

1 -ϕt - 1� θaθa - θe

; or;ϕt - 1⩽σðθa - θeÞ

σðθa - θeÞ + θa : □

Received 02 March 2012;accepted 22 July 2013 after two revisions

2Assume the boundary condition that σt(0)= 0.

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