managing commitments in multiple concurrent negotiations · 2019. 12. 9. · managing commitments...

Electronic Commerce Research and Applications 4 (2005) 362–376

www.elsevier.com/locate/ecra

Managing commitments in multiple concurrent negotiations

Thuc Duong Nguyen a,*, Nicholas R. Jennings b

a MLB1, PP12, B62 Orion Building (B62-MH), Adastral Park, Martlesham Heath, Ipswich IP5 3RE, UKb School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK

Received 14 April 2005; received in revised form 2 June 2005; accepted 28 June 2005Available online 22 July 2005

Abstract

Automated negotiation by software agents is a key enabling technology for agent mediated e-commerce. To this end,this paper considers an important class of such negotiations – namely those in which an agent engages in multiple con-current bilateral negotiations for a good or service. In particular, we consider the situation in which a buyer agent islooking for a single service provider from a number of available ones in its environment. By bargaining simultaneouslywith these providers and interleaving partial agreements that it makes with them, a buyer can reach good deals in anefficient manner. However, a key problem in such encounters is managing commitments since an agent may want tomake intermediate deals (so that it has a definite agreement) with other agents before it gets to finalize a deal at theend of the encounter. To do this effectively, however, the agents need to have a flexible model of commitments thatthey can reason about in order to determine when to commit and to decommit. This paper provides and evaluates sucha commitment model and integrates it into a concurrent negotiation model.� 2005 Elsevier B.V. All rights reserved.

Keywords: Agents; Automated negotiation; Commitments; Concurrent negotiation

1. Introduction

Automated negotiation is a key form of interac-tion in agent-based systems and such negotiationsexist in many different forms [1]. In this paper, wefocus on one such form, namely one-to-manynegotiations in service-oriented contexts. Here, a

1567-4223/$ - see front matter � 2005 Elsevier B.V. All rights reserv

doi:10.1016/j.elerap.2005.06.005

* Corresponding author.E-mail addresses: [email protected] (T.D. Nguyen),

[email protected] (N.R. Jennings).

service is simply viewed as an abstract representa-tion of an agent�s capability. This view is nowwidespread in a range of domains that we are tar-geting for our work, including the web, the grid,pervasive computing and e-business [2]. In moredetail, one agent is seeking to provision a singleservice (described by multiple attributes, such ascost, time, quality, etc.) from a number of poten-tial providers. Traditionally, this type of encounteris handled via some form of single-sided (reverse)auction protocol. However, in previous work, we

ed.

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mailto:[email protected]

T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 363

introduced multiple, concurrent bilateral negotia-tions as an alternative [3,4]. Our approach offersa number of advantages over its more traditionalcounterpart (especially in the time-constrainedenvironments that motivate our work).

� First, in most reverse auctions, the buyer is onlyallowed to select an agreement from the set pro-posed by the sellers. On the other hand, thebuyer in our approach can also send proposalsand counter-proposals. For multi-dimensionalcontracts, this two way communication isimportant because it allows the buyer to pro-vide an indication of the areas of the searchspace where it would like to see the agreementslie. Furthermore, the buyer in our approach candeploy different strategies when bargaining withdifferent types of providers. This variabilitymeans negotiation can be tailored to the indi-vidual opponents (e.g., some opponents maybe known to be desperate to obtain a deal),rather than derived implicitly through thecompetition of the sellers (as happens in thetraditional auctions). Also, the agreementreached in one thread can be used to influencenegotiation behavior in other threads. Thisgives the buyer additional strategic information(and hence bargaining power) that can beexploited to obtain better deals.

� Second, the time at which an agreement isreached in the multiple concurrent negotiationcase can be reduced. For auctions that do nothave deadlines, the end time is indeterminatewhich is unacceptable for our time-constraineddomain. In auctions where there is a deadline,no agreement can be reached before this time.On the other hand, by using multiple concur-rent negotiations, deals are likely to be availablebefore the overall deadline and if these aredeemed satisfactory the agent may decide to ter-minate other negotiations (perhaps sacrificingsome potential gain) in order to take benefitfrom the agreed deal more quickly.

Despite these advantages, however, the negotia-tion protocol in our previous approach was some-what unrealistic since it was heavily biased in favorof the buyer. Thus, during the negotiation, the

buyer agent could make a number of intermediate

deals with various sellers (where each such deal is atemporary agreement with a specific seller). Then,when its deadline is reached, the buyer selects themost profitable deal as the final agreement anddeclines others. It can operate in this way becausethese intermediate deals are assumed to be bindingon the sellers (meaning they are not allowed torenege from deals once committed) but not onthe buyer. Although these unbreakable commit-ments make it easier for the buyer to achieve gooddeals, it is highly disadvantageous for the sellers.Thus, in order to be applicable in realistic negoti-ation situations, the model needs to be extendedso that it can deal with situations in which the pro-viders can also renege from deals. To deal with thissituation, we develop a commitment manager andan associated reasoning model that enables theagent to behave in a flexible and efficient manner.

To date, a number of commitment models havebeen developed, each with its own advantages anddisadvantages (see Section 4 for more details). Webase our model on the notion of leveled commit-

ment contracts [5] in which an agent can decommit(for whatever reason) simply by paying a decom-mitment fee to the other agent. In so doing, ourwork advances the state of the art in the followingways. First, it allows the participating agents to beable to renege from deals whenever they deemappropriate, simply by paying a decommitmentfee to their counterparts. Since the providers areno longer forced to be tied to their commitments,they have greater freedom in their behaviors.Second, the agents in our model have differentdeliberation mechanisms for various penaltylevels, thus, they can flexibly perform in a widevariety of e-marketplaces. Finally, our commit-ment model allows the buyer agent to have atrade-off between the number of agreements itmakes and their utility values. This capabilityhelps it to effectively select different commitmentstrategies according to its purchasing objectives.

The remainder of the paper is organized asfollows: Section 2 details our new bargaining modeland Section 3 presents the initial experimentalresults. Section 4 relates the model to current workin the field and, finally, Section 5 presents theconclusions.

Thread 1

Thread 2

Thread n

Seller 1

Seller 2

Seller n

Buyer Agent

decline

accept

Coo

rdin

ator

C

omm

itmen

tM

anag

er

offer

counter-offer

Fig. 1. System architecture.

364 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376

2. The negotiation model

The foundation of this work is the concurrentnegotiation model outlined in [4]. Building on this,the main contribution of this paper is the integra-tion of the ability to reason about commitmentand decommitment for the intermediate agree-ments. Before we can focus on this new ability,however, we first need to recap the basic architec-ture of our model.

In more detail, the agent that wishes to pur-chase the service is called the buyer and the agentsthat are capable of providing the service are calledthe sellers. Service agreements (contracts) areassumed to be multi-dimensional. The buyer hasa hard deadline tbmax by when it must conclude itsnegotiations for the service. This deadline is alsothe time when the service will be performed bythe chosen seller. Similarly, each seller a has itsown (private) negotiation deadline tamax . All agentshave their own preferences about the service andthis information is private. Each agent has a rangeof strategies (S) that it can adopt1 and its choice ofstrategy is also private information. Each negotia-tion thread (bargaining with a particular seller)follows a Sequential Alternating Protocol [7]where at each step an agent can either accept theoffer from the opponent, propose its counter-offer,renege from its commitment or opt out of thenegotiation (typically if its deadline is reached).

In more detail, the model for the buyer agentconsists of three main components: a coordinator,a number of negotiation threads and a commitment

manager (see Fig. 1). The negotiation threads dealdirectly with the various sellers (one per seller) andare responsible for deciding what counter-offers tosend to them. The coordinator decides the negoti-ation strategies for each thread. After each round,the threads report back their status to the coordi-

1 Given the time-constrained nature of our encounters, thetypes of strategy that we consider are the time-dependent familyintroduced in [6]. These can be broadly divided into threeclasses: the conceder strategy quickly lowers its value until itreaches its reservation (minimum acceptable) value. The linear

strategy drops to its reservation value in a steady fashion.Finally, the tough strategy keeps its value until the deadlineapproaches and then it rapidly drops to its reservation value.

nator. If a thread reaches a deal with a particularseller, it terminates its negotiation and waits untilthe deadline tbmax is reached. The coordinator willthen notify all other negotiation threads of thenew reservation value and it may change the nego-tiation strategy for some of them. The commit-ment manager, which is newly introduced in thiswork, handles any issue that is related to commit-ment and decommitment. It is involved when athread needs to decide whether or not to accepta proposed offer (it makes the decision based onthe buyer�s current commitment and its commit-ment strategy; see Section 2.3 for more detail) orwhen a seller decides to renege from a committeddeal (it updates its status accordingly). The resultof the commitment manager (either accept orreject) will be passed through the coordinator forcross checking with other threads before gettingback to the calling thread. The detailed workingof the three components are described in thefollowing subsections.

2.1. The coordinator

The coordinator is responsible for coordinatingall the negotiation threads and choosing an appro-priate negotiation strategy for each thread. Beforestarting a negotiation, the coordinator considersthe available information about the types of thesellers that are in the environment. In our case,we consider that seller agents can be of the follow-ing types: conceder (i.e., they are willing to concedein search for deals) or non-conceder (i.e., they tend

Initialize

Make offer and propose

Wait for reply

Got notified

Process the notification

Terminate

yes

Report back tothe coordinator

counter-offer

accept

Change thereservation

value/strategy

no

withdraw

Fig. 2. A single negotiation thread.


to negotiate in a tough manner). The set of avail-able agent types is denoted as Atypes: types ={con,non}. This information is represented as aprobability distribution over the agent types,which may be based on past experiences, obtainedfrom a trusted third party, or from a system ofreferrals [8]. If no such information is available,all agents are assumed to have a uniformdistribution.

There are two further sources of informationthat aid the coordinator�s decision making: thepercentage of success matrix (PS) and the pay off

matrix (PO). The former measures the chance ofhaving an agreement as the outcome of the negoti-ation when the buyer applies a particular strategyto negotiate with a specific type of the seller. Thelatter measures the average utility value of theagreement reached in similar situations.

Given this information, the coordinator calcu-lates the probability of the first seller (a randomlypicked agent from those that will be negotiatedwith for the service in question) being of a specifictype. Based on this, the agent calculates theexpected utility of applying the various strategiesat its disposal for this particular seller and selectsthe one that maximizes this value. Formally, theexpected utility EU(k) for strategy k 2 S is calcu-lated as

EUðkÞ ¼X

a2Atypes

PSðk; aÞPOðk; aÞPðaÞ; ð1Þ

where P(a) is the probability that the seller agent isof type a and PS and PO are the values in the cor-responding matrices, respectively. After finishingwith the first seller, the coordinator uses a Bayes-ian update function to update the probability dis-tribution of the agent types and continues on withthe second seller. This process is repeated until thecoordinator finishes allocating the strategies to allthe negotiation threads (see [4] for more details).

The other task of the coordinator is to classifythe sellers during negotiation and to change thenegotiation strategies for the threads. Specifically,the buyer attempts to characterize the sellers,based on the utility value of their proposals, intothe sets Acon, Anon. Thus, at time t: 2 < t 6 tbmax ,called the analysis time, the coordinator tries todetermine if a given seller is a conceder or a

non-conceder. In particular, assume U(a,t 0) is theutility value of the offer that seller agent a madeat time t 0:(1 6 t 0 6 t), according to the buyeragent�s preferences. Then seller a is considered aconceder if 8t0 2 ½3; t� : Uða;t0Þ�Uða;t0�1Þ

Uða;t0�1Þ�Uða;t0�2Þ > h where his the threshold value set on concessionary behav-ior. If this condition is violated, seller a is consid-ered a non-conceder.

Now, given the set of strategies S and the set ofclassified seller agents As, the coordinator changesthe strategy for each negotiation thread based onthe type of the agent it believes it is negotiatingwith. Specifically, for each agent a 2 As, the coor-dinator selects the strategy k 2 S that provides themaximum expected utility and applies it to thecorresponding thread, using Eq. (1), with

P ðj 2 AtypesÞ ¼1 if a is of type j

0; otherwise.

�

2.2. The negotiation threads

An individual negotiation thread is responsiblefor dealing with an individual seller agent onbehalf of the buyer. Each such thread inherits itspreferences from the buyer agent and has its nego-tiation strategy specified by the coordinator. Thestructure of a negotiation thread is presented inFig. 2. Specifically, each thread is composed ofthree subcomponents, namely communication (rep-resented by the dotted lines), process (representedby the bold lines) and strategy (represented bythe normal lines). The communication subcompo-nent is responsible for communicating with the


coordinator and the commitment manager. Beforeeach round, it checks for incoming messages fromthe coordinator and if there are any, it passes themto the process subcomponent. After each round, itreports the status of the thread back to the coordi-nator. The process subcomponent deals withmessages from the communication subcomponent.This can either be changing the reservation valueor changing the strategy. The strategy subcompo-nent is responsible for making offers/counter-offers, as well as deciding whether or not to acceptthe offer made by the seller agent (by cooperatingwith the commitment manager).

2.3. The commitment manager

Each time the buyer and a seller a decide toagree on an intermediate deal with utility valueU(a,t) (according to the buyer�s preferences), thisdeal is binding on both agents. If either of themdecides to break the contract, it has to pay adecommitment fee (q) to its opponent. This fee isdynamically calculated as a percentage of theutility of the deal2 and is also based on the timewhen the contract is broken.3 To this end, the func-tion to calculate the decommitment fee at timet < tbmax is chosen as follows:

qðtÞ ¼ Uða; tÞ � q0 þt � ta

tbmax � ta� ðqmax � q0Þ

� �;

ð2Þwhere ta is the contract time, when the deal isagreed upon, q0 is the initial penalty (the fee topay if the deal is broken at contract time, ta) and

2 Traditionally, there are two ways of calculating the decom-mitment fee, namely fixed value (all contracts have the samefixed decommitment fee that is decided prior to the negotiation)and percentage of contract value (the fee is defined as apercentage of the utility value of the contract). It has beenempirically demonstrated that the latter type allows the agentsto be more flexible in deliberating about their behaviors andenables them to gain a higher utility value than the former [9].Consequently, we use the percentage of contract value in ourmodel.3 This factor is incorporated to discourage the agent from

dropping its commitment towards the end of the negotiation(where it is more difficult to draft in a replacement). Conse-quently, the later an agent decommits, the more it has to pay.

qmax P q0 is the final penalty (the fee if the dealis broken at execution time, tbmax ).

By means of an illustration, consider the fol-lowing example. Assume the buyer�s deadlineðtbmaxÞ is 10, the initial penalty (q0) is 5% and thefinal penalty (qmax) is 10%; a deal with theexpected utility value 0.58 was made at time 6.At time 9, if the buyer wants to decommit, by(2), it has to pay

qðtÞ ¼ 0.58� 0.05þ 9� 6

10� 6� ð0.10� 0.05Þ

� �

¼ 0.58� 0.0875 ¼ 0.05075.

Since the buyer agent now has to pay a fee everytime it breaks a contract, it cannot simply just agreeon all deals and, later, select the highest value dealas the final agreement (as it did in the originalversion of our model). Thus, when presented witha potential agreement from a specific seller, thebuyer has to decide whether it should take this dealor reject it. In some cases, by rejecting this agree-ment and, later on, committing to another deal,the buyer will gain a better utility value (see Section3 for more details). To capture this, when presentedwith a contract /(a) that has utility value of U(a,t)from seller a at time t, the buyer will accept /(a) asan intermediate deal (and renege on its currentcommitment, if one exists) if all of the followingconditions are satisfied:

1. If it already has a commitment with anotheragent a 0 at time ta 0 and this deal has not beenbroken, the utility gained by taking this newoffer must be greater than that of the currentdeal, after having paid the decommitment fee.This means U(a,t) > U(a 0,ta 0) + q(t).

2. The degree of acceptance (l) for /(a) must beover a predefined threshold (s). This thresholdspecifies how the buyer should accept the offers,whether it is greedy (tends to accept any possi-ble deal) or patient (only deals that provide acertain expected utility value will be accepted).l is calculated by comparing the utility valueof /(a) with the predicted utility value of thenext set of contracts from other sellers, alsotaking into account the relation between thecurrent time and the buyer�s deadline. Specifi-cally, the formula for calculating l is


lð/ðaÞÞ ¼ Uða; tÞ � qðtÞmaxfU expðai; tÞjai 2 As n ag

� ttbmax

;

ð3Þwhere q(t) is the decommitment fee that the buyerhas to pay if it has already committed to a dealwith another seller (if it has not, q(t) is consideredto be 0) and Uexp(ai,t) is the predicted utility of thenext proposal from seller ai. The value of Uexp(ai,t)is calculated as:

U expðai; tÞ ¼ Uðai; tÞ þdUðt; t � 1Þ

dUðt � 1; t� 2Þ � jdUðt; t � 1Þj;

ð4Þ

where dU(t1,t2) is the distance, in terms of utilityvalue, between two offers of seller ai at time t1and t2: dU(t1,t2) = U(ai,t1) � U(ai,t2).

To illustrate the operation of the commitmentmanager in more detail, consider the followingexample. There are 4 participating sellers, thebuyer�s deadline (tbmax ) is 6, the initial penalty (q0)is 10%, the final penalty (qmax) is 20% and thethreshold (s) is 0.8. The buyer has committed ona deal with seller 4 at time 2 with the expectedutility value of 0.21. The utility values of previousoffers from all the sellers are displayed in Table 1.

At time 3, the buyer has to decide whether itwill accept the offer /(a3) from seller a3. Since itis already committed to a deal with a4, if it wantsto take /(a3), it will have to pay a decommitmentfee to a4. By (2), the fee it has to pay is

qð3Þ ¼ 0.21� 0.1þ 3� 2

6� 2� ð0.2� 0.1Þ

� �¼ 0.026.

As can be seen, U(a3,3) < U(a4,2) + q(3), so thefirst condition is violated. Thus, the buyer willreject /(a3) and remain with its commitment witha4.

Table 1Utility values of the offers

Agent t = 1 t = 2 t = 3

a1 0.03 0.12 0.16a2 0.01 0.04 0.10a3 0.1 0.19 0.23a4 0.11 0.21 –

At time 4, however, seller a4 decides to renegeon its current deal and pay the decommitmentfee to the buyer. According to Eq. (2), it has to pay

qð4Þ ¼ 0.21� 0.1þ 4� 2

6� 2� ð0.2� 0.1Þ

� �¼ 0.0315.

As can be seen, this decommitment from a4leaves the buyer with no agreement. Now, at time5, the buyer has to decide if it should take up theoffer from a1 (Table 2 shows the utility values ofthe offers from all the sellers). Since it has no inter-mediate agreement, the first condition is satisfied.To evaluate the second condition, the buyer firstcalculates the value for Uexp(a1,5) and Uexp(a2,5)using (4):

U expða2; 5Þ ¼ 0.26þ�0.04

0.2� 0.04 ¼ 0.252;

U expða3; 5Þ ¼ 0.36þ 0.05

0.08� 0.05 ¼ 0.391.

The value of l(/(a1)) is then calculated, using Eq.(3), as

lð/ða1ÞÞ ¼0.4

0.391� 5

6¼ 0.852.

This time, since l(/(a1)) > s, the buyer will committo this deal. It keeps on bargaining in this wayuntil its deadline is reached. If, at that time, thereis an intermediate deal that has not been broken,this deal is selected as the final agreement. If,however, no such deal exists, the negotiation isconsidered unsuccessful and terminated withoutan agreement.

Up until this point, we have only considered thesituation where the buyer agent commits to amaximum of one intermediate contract at onetime. However, it possible for the buyer to committo more than one contract at any one time andthen, later, select the best one and decommit fromthe others. This represents a cautious approach

Table 2Utility values of the offers (cont.)

Agent t = 1 t = 2 t = 3 t = 4 t = 5

a1 0.03 0.12 0.16 0.28 0.4a2 0.01 0.04 0.10 0.30 0.26a3 0.1 0.19 0.23 0.31 0.36a4 0.11 0.21 – – –

Table 3The independent variables

Variables Descriptions Values

q0 The initial penalty fee [5,100]qmax The final penalty fee (qmax P q0) [5,100]


and avoids the risks associated with committing toonly one contract which is then revoked near thedeadline, leaving the agent with insufficient timeto find a replacement. The downside of thisapproach, however, is that if the sellers do notrenege, the buyer may end up paying a significantpart of its utility value as the penalty fee. Never-theless, in some cases, it may be beneficial for thebuyer to consider the option of having multiplecommitments during the bargaining process. Tocapture this, assume that the maximum numberof commitments that the buyer will hold at anyone time is x P 1 and let X = {Ci|i 2 [1,x]} bethe set of contracts that the buyer is currentlycommitted to: |X| 6 x. Here, Ci = {/ 0,t 0} is thecontract that consists of an intermediate deal / 0

that has been agreed at time t 0. Assuming that attime t, there is an offer / from seller k that hasl(/(k)) > s (see Eq. (3))4 and U(/(k),t) > U(/ 0,tk 0) + q(t) "C(/ 0,tk 0) 2 X then this offer will thenbe accepted by the buyer. This, in turn, meansthe following steps will be taken:

1. If X is not full (i.e., |X| < x), C(/,t) will beadded to X: X = X\C(/,t).

2. If X is full (i.e., |X| = x) select C(/ 0,tk 0) 2 Xthat has the minimum value of U(/ 0,tk 0) anddecommit from that contract. Then, C(/,t) willbe added to X: X = X\C(/,t).

Now if a seller k that has a contract C(/(k),tk)decides to withdraw its commitment, that contractwill be subtracted from X: X = XnC(/(k),tk).Then at the end of the bargaining process, if thereis more than one contract in X, the buyer simplyselects the one that has the highest utility valueas the final agreement and decommits from allthe others.

s The l threshold [0,1.5]x The number of concurrent commitments [1,4]

Table 4The dependent variables

3. Empirical evaluation

Having introduced the commitment manager,the next step is to evaluate its effects on the model.

4 If |X| < x, q(t) is considered to be 0. If not, q(t) is thepenalty the buyer will have to pay to break from the contractC(/ 0,tk 0) 2 X that has the minimum value of U(/ 0,tk 0).

We choose empirical evaluation as the method ofmeasurement for a number of reasons. First,because our model is heuristic in nature, it is diffi-cult to make meaningful theoretical predictions.Second, there are a number of internal variablesthat control the behavior of the model, as well asexternal variables that define the environment inwhich the model is being used. These variablesare interrelated and need to be considered in abroad range of situations. Empirical techniquesallow us to manipulate these variables, conductthe experiments and analyze the results.

3.1. Experimental setup

In more detail, we use the exploratory studies

evaluation technique [10]. With this method,general hypotheses are formed to express theintuitions about the causal factors within themodel. The experiments are then conducted andgenerate the results that either support thesehypotheses or go against them. In our evaluation,the independent variables are given in Table 3 andthe dependent ones are listed in Table 4.

Apart from the control variables described inTable 3, other control variables are selected asper [11]. Specifically, the number of seller agents(n) is set in the range of [1, 30] and the number ofnegotiation issues (m) is set in the range of [1, 8].An agent a�s preference for issue j is representedby the tuple fxajmin

; xajmax;wa

jg. The tuple ½xajmin; xajmax

�

Variables Descriptions

U The utility value of the final agreementN The number of successful negotiationsD The number of decommitments made by buyer

T.D. Nguyen, N.R. Jennings / Electronic Commerce

is an interval independent variable, whose scale isinfinite. To simplify the analysis, therefore, weassume all issues have the same domain of valuesand we randomly set the value for xajmin

to be inthe interval [0, 20] and xajmax

to be in the interval[30, 50]. The values for wa

j are set to give all issuesequal importance. The negotiation deadline foreach agent is an ordinal independent variable,whose value is randomly chosen, ranging from 5(very short deadline) to 50 (long deadline). Thepenalty fee (both initial and final) is also an ordinalindependent variable, whose value is randomlychosen, ranging from 5% (small) to 100% (equalto the value of the contract). Similarly, the s thresh-old is either 0 (meaning the buyer is greedy and willcommit to any intermediate deal that it can gethold of) or 0.5 (meaning the buyer is patient andwill only engage on a deal that provides highexpected utility value).5

The seller agents in this evaluation are charac-terized in a similar fashion to ones set up in ourprevious experiments [4]. Specifically, they arecharacterized by three independent variableswhose values are set in the following manner:

� The values� domain for the set of negotiation

issues: These domains are randomly generated(from the same distribution as the buyer agents�values) so that each domain intersects with thecorresponding domain of the buyer�s preference.For example, if the buyer�s value domain for anissue j is ½xbjmin

; xbjmax� then the corresponding value

domain for seller awill be generated as ½xajmin; xajmax

�that satisfies xbjmin

6 xajmin6 xbjmax

6 xajmax.

� The negotiation strategy: Each seller is assigneda random strategy selected from a predefinedset of alternations (as outlined in [6]). This setis composed of time-dependant functions (likeconceder, boulware and linear) and behavior-dependant tactics (such as tit-for-tat in its vari-ous forms).

� The negotiation deadline: The deadline for eachseller is generated from the same distribution asfor the buyer.

5 Future work will investigate in more detail how this valueaffects the outcome of the model.

The only difference is that now if a seller hascommitted to a deal, it has a chance of being madean outside offer with the utility value of 1.0 (whichis the highest possible utility value). Thus, there isa probability that it will decommit. To this end, weconsider three types of sellers:

� Loyal: once a seller has committed to an inter-mediate deal, it will not renege from it.

� Loose: a seller always breaks a committed dealif it is presented with a better option.

� Partial: if a seller finds a better option, it willbreak a committed deal with a percentage ofprobability (as per [12]). In this experiment,we set this percentage to be 50%, meaning thathalf of the time a seller finds a better deal, it willrenege and half of the time it will stay with itscurrent deal.

After each experiment, we measure the utilityvalue of the final agreement for the buyer (U). Inour evaluation, the utility of an offer X ={x1,x2, . . . ,xm} to an agent a is calculated as

UðX Þ ¼Xmj¼1

waj �

xj � xajmin

xajmax� xajmin

.

We also measure the number of agreementsreached at the end of the negotiation encounter(N) and the average number of decommitmentsthat the buyer made (D). In all cases, the resultsare gathered from a series of experiments in differ-ent environment settings. Each experiment consistsof 1000 runs and the results are averaged and putthrough a regression test to ensure that all differ-ences are significant at the 99% confidence level.

Research and Applications 4 (2005) 362–376 369

3.2. Experimental hypotheses

We now turn to the specific hypotheses.

Hypothesis 1. When dealing with loose or partialsellers, the higher the penalty fee is, the lower thenumber of final agreements reached by the buyer.

To evaluate this hypothesis, we measure thenumber of final agreements achieved with varyingtypes of seller agents (see Fig. 3). As can be seen,the number of final agreements reached by the

Fig. 3. Number of successful negotiations for varying penaltyfee.

Fig. 4. Final utility value for varying penalty fee.


buyer is dramatically reduced as the penalty fee isincreased. Specifically, when dealing with loosesellers, around 97% of the negotiations are success-ful when the penalty fee is 5%. As the penalty feeincreases to 100%, this success rate drops downto only 84%. Similarly, the figures when dealingwith partial sellers are 98% and 92%, respectively.This decreasing trend is explained by the delibera-tion mechanism of the buyer. Specifically, assumethat the buyer has already made a commitmentwith seller k and now it is presented with anotheroffer from seller k 0. If it decides to take this newoffer from k 0, it will have to pay k a decommitmentfee q. As the penalty fee is increased, so is q. Thus,in some cases, the buyer cannot afford to take thisnew offer and it has to stay with its commitment tok. Later on, if k decides to break its commitment,the buyer is left with no intermediate agreement.As such, there may not be enough time for thebuyer to find another replacement deal and, thus,no final agreement can be reached. On the otherhand, if the buyer can take the offer from k 0, theprobability that k 0 will renege is less than that ofk. Thus, a final agreement can be reached.

Another observation is that the more loyal theseller is, the greater the number of final agreementsthat the buyer makes. This difference is caused bythe probability of the sellers breaking theircommitments. Since a loyal seller never reneges,once it has committed, its contract is kept untileither it is declined by the buyer or it is selected

as the final agreement. Therefore, once an interme-diate deal is reached, a final agreement is alwaysguaranteed to exist. However, this is not the casefor the other types of sellers. Once they have com-mitted, it is not guaranteed that they will actuallystay faithful with their commitments. If a sellerbreaks a contract, the buyer has to find a replace-ment. If it fails to do so, no final agreement will beachieved. Thus, the less loyal the sellers are, thefewer chances there are for the buyer to reach afinal agreement.

Hypothesis 2. The higher the penalty fee, thelower the utility of the final agreement gained bythe buyer.

As can be seen from Fig. 4, this trend is true forall seller types. Specifically, when dealing withloose sellers, the average utility of the final agree-ment for the buyer drops from 0.61 to 0.46 whenthe penalty fee goes from 5% to 100%. The corre-sponding figures for partial and loyal sellers are0.62–0.43 and 0.63–0.40, respectively. The reasonfor this decrease in the final utility value is thatthe higher penalty fees mean more chance thatthe buyer will commit to an early agreement (andstay with this commitment until either its deadlineis reached or the corresponding seller decides torenege). These early commitments by the buyerhave two main effects. First, such agreements tendto have lower utility value for the buyer, comparedto the contracts that are offered at a later stage (thebuyer cannot afford to take these contracts due to


high decommitment fees). Second, once that com-mitment is later broken, the buyer will have to finda replacement. Even if it is successful in findingone, since there is not much time for bargaining,the utility value of this newly found agreement islikely to be less than that of the previous deal.Consequently, the utility gained by the buyer isreduced.

Furthermore, with increasing penalty fee, themore loyal the seller, the lower the value of thefinal agreement gained by the buyer (see Fig. 4).The reason for this observation is because thebuyer benefits from the decommitment fee gainedwhen a seller reneges from a committed deal. Asper our experimental setup, loose sellers decommitmore often than partial sellers and loyal sellersnever renege. Thus, as the penalty fee increases,the buyer will benefit more when dealing with lessloyal sellers.

Hypothesis 3. Thebuyer decommits less frequentlyas the penalty fee increases.

Fig. 5 shows the average number of decommit-ments made by the buyer for varying penalty feesand different seller types. Since the buyer�s deliber-ation includes the decommitment fee it has to payif it want to replace its current intermediate deal(see Eq. (2)), the less it has to pay, the more favor-able it will be to take up a better deal. Thus, evenwhen a seller offers an intrinsically higher valuecontract than the current deal it has, the buyer

ρ ρ

Fig. 5. Number of buyer�s decommitments for varying penaltyfee.

may be better off sticking with its existing commit-ment in order to avoid paying a hefty fine. This iswhy the buyer almost never reneges when thepenalty fee is close to 100%.

Hypothesis 4. The more patient the buyer, thehigher the utility for the final agreement. However,the chance of having a final agreement is reduced.

We start by looking at the performance of themodel with a number of different values for thedegree of acceptance (specifically s2 [0.1,1.5]). Forsimplicity, we fix the penalty fee value at (q0 = 5,qmax = 10) and assume we are dealing with partialsellers. These values are chosen just to give us anidea of how the results could potentially be and adetailed analysis will follow. The results are dis-played in Fig. 6.

As can be seen, as the value of s increases, theutility value for the final agreement decreases. Thisis because in a particular negotiation, if the buyertends to ignore the current offer from the seller, infavor of a higher value one at a later time, there isa possibility that a high value offer will not beforthcoming (e.g., the seller may run out of timeor be at the limit of its reservation values). Thus,towards the end of the encounter it will have tosettle for a lower value deal (because this is betterthan no deal). This, in turn, puts a downwardtrend on the final utility value achieved.

On the other hand, the number of final agree-ments reached increases as the value of s increasesup to 0.5, then it decreases. Now, since we are

Fig. 6. Performance vs. degree of acceptance.

Fig. 7. Final utility value for varying penalty fee.

Fig. 8. Number of successful negotiations for varying penaltyfee.


dealing with partial sellers, if they are presentedwith a better outside offer, they have the chanceto renege and may leave the buyer with no agree-ment at hand. When the value for s is small (lessthan 0.5 in this case), the buyer tends to take upany offers that are available to it at an early time.Later, when the seller that is sharing the commit-ment with the buyer decides to back down, theremight not be enough time for the buyer to recoverfrom this loss and, thus, it might end up with noagreement at the end of the encounter. However,if it is too strict on accepting intermediate deals,it also risks the chance of having obtained no dealat all. This is the situation when the value of sincreases past 0.5. From Fig. 6, it can be seen thatby setting value of s at around 0.5, the buyer willachieve the highest number of final agreementswith a reasonably good final utility value.

We extend the aforementioned result by com-paring the results of having two different valuesfor s: greedy (s = 0) and patient (s = 0.5) in theexperiments with different penalty values, as wellas different seller types. Recall, the greedy buyerwill commit to any offer that it can take (if it ismore beneficial than the one it currently has, tak-ing into account the decommitment fee it will haveto pay). In contrast, the patient buyer will onlycommit to an offer that has significantly greatervalue (compared with the one that it currentlyhas). As it only accepts higher value contractscompared to its counterpart, the patient agents�final agreements always have higher utility valuethan those of the greedy agent (see Fig. 7).

Now, not only does the patient agent gain higherutility value, the number of successful agreementsachieved is also higher than or, at least, equal tothat of the greedy agent (see Fig. 8). The reasonfor this is related to the way an intermediate agree-ment is accepted by the buyer. The greedy buyeraccepts a higher number of intermediate agree-ments than its counterpart.6 Thus, its chance ofhaving an agreement reneged upon is higher thanthat of the patient agent. In some cases, this decom-mitment limits the chance of the buyer of having an

6 The greedy buyer accepts any possible agreement, whereasthe patient one only accepts agreements that have a significantlygreater value compared with the one that it currently has.

agreement at the end of the negotiation. Conse-quently, the patient agent will be able to reachmore agreements than the greedy one at the endof the bargaining process.

However, even though it can gain better utilityvalue than its greedy counterpart, the patient agentmanages to get fewer agreements than its counter-part. This is because the patient agent only acceptsa deal if the degree of acceptance (l) of this deal isgreater than a threshold (in this case, s = 0.5).Thus, not all the deals proposed by the sellerssatisfy this condition. Indeed, in some cases, noneof the proposed contracts satisfy this condition.This limits the chance of the buyer having anagreement at the end of the negotiation. On the


other hand, the greedier the agent is, the higher thechance that an offer will be accepted. Conse-quently, the greedy agent will be able to reachmore agreements than the patient one at the endof the bargaining process.

Hypothesis 5. When dealing with loyal sellers, thebuyer is better off committing to a maximum ofone contract at any one time. For other sellertypes, the buyer should commit to a maximum oftwo contracts.

Fig. 9 shows the number of agreements obtainedby the buyer at the end of the encounter when itvaries the number of commitments it can hold atany one time (here x 2 [1, 4]). As can be seen, whenholding more than one commitment, the buyerincreases its chance of reaching an agreement whendealing with non-loyal sellers. In particular, whenx is increased from 1 to 2, the buyer gains 0.9%more final agreements when dealing with partialsellers and 2% more when dealing with loose sell-ers. This improvement can be explained simplyby looking at the behaviors of the sellers. As thesellers are not loyal, when presented with an out-side offer, they may renege. If this happens nearthe end of the negotiation process and the buyercan only commit to a single contract, it will leavethe buyer very little time to find an alternative(and in some cases it will not be able to do so).On the other hand, if the buyer is holding morethan one contract and an agent reneges then it

Fig. 9. Number of agreements vs. buyer�s maximum commit-ments.

has something that it can fall back on and it is lessvulnerable to being left with no agreement. Forvalues of x > 2, however, the improvement iscomparatively minor because when the buyer iscommitting to more than one contract, the chancethat all the sellers renege is significantly reducedcompared to the situation when the buyer can onlyhave one commitment at a time. This, in turn, has avery slight impact on the number of agreementsachieved.

The final utility achieved by the buyer withvarying values for x is displayed in Fig. 10. Ascan be seen, when x > 2, the utility gained is dra-matically reduced (8% decrease when x goes from2 to 3 and 16% decrease when x goes from 3 to 4).This is because if a buyer agent has more contractsat the end of the negotiation process, it will end uppaying a significant penalty fee for breaking them.When x = 2, the situation is similar to that ofdealing with loyal sellers. However, when negotiat-ing with partial or loose sellers, x = 2 gives similarresults and, in some cases, is better than setting xto 1. The reason for this is because as the non-loyalseller agents can renege on their commitments andif they do so towards the end of the negotiationprocess, the buyer will gain additional penalty feesfrom those sellers and is still left with at least oneintermediate contract in hand. Thus, at the end, itis still able to have the final agreement, but it doesnot have to pay a decommitment fee to any otherseller agent.

Fig. 10. Final utility value vs. buyer�s maximum commitments.


As can be seen, when dealing with loyal sellers,the buyer does not necessarily need to have morethan one commitment since it can be sure thatthe sellers will never renege from their deals. How-ever, when dealing with partial or loose sellers, thesituation is different. The greater the number ofcommitments it holds, the higher the number offinal agreements it is likely to obtain. Nevertheless,the final utility value reached is decreased becauseit will have to pay a large amount of penalty fees todecommit from these commitments. To this end,the buyer is best setting x to 1 when dealing withloyal sellers and x to 2 when dealing with othertypes of seller to ensure that it will achieve highestpossible utility value together with an acceptablenumber of final agreements.

4. Related work

Traditionally, once a contract is made in a nego-tiation, it is binding on all participants. Neitherparty can back out no matter what happens inthe future [13–15]. This is also the case for existingconcurrent negotiation models [4,16,17]. However,this view is very limiting for the agents and it maylead to irrational and inefficient behavior [12]. As aresult, a number of methods have been developedto overcome this limitation.

One of the first pieces of work in this area wasthe contract net protocol [18], where there is a pos-sibility for a decommitment. Here, the contracteragent could send a termination message to cancelthe contract, even when a part of it has been ful-filled by the contractee. As the agents participatingin a contract net are generally assumed to be coop-erative, they do not mind losing their effort (evenwithout any form of compensation). In a similarfashion, the role of commitment for cooperativeagents was examined in the context of automatedscheduling of meetings [19]. In e-commerce set-tings, however, these models are inappropriatebecause the agents are not always cooperativeand they seek to maximize their individual gains.

For self-interested agents, contingency contractshave been introduced as a method of allowingthem to break commitments [20]. In this case, anagent�s commitment to a contract is made contin-

gent on specific future events. Thus, if these speci-fied contingencies aries, the agents are allowed todrop their commitments [21]. However, there area number of problems associated with this typeof contract [5]. First, not all possible future eventsare known to the agents beforehand, thus, theycannot always make optimal use of contingencycontracts. Second, this type of contract is usefulwhen the number of future events is small. If, how-ever, this number increases, it is cumbersome oreven impossible for all the events to be monitored.Furthermore, these events may not affect the origi-nal contract independently, they may have a com-bined effect on the value of the contract [13]. As aresult, this approach is not adopted in our work.

The most advanced work in the area, and alsothe basis to our work, is the leveled commitment

contracts (LVC) [5]. Our commitment manager isbuilt upon the same basic intuition that any agentcan freely decommit from a contract, for whateverreason they deem appropriate, by simply paying adecommitment fee to the other partner. However,our model is different in a number of importantways. First, the original LVC only covers a twoperson game. We have extended this to cover themultiple providers found in our target environ-ment. Second, we do not just reason about decom-mitment, we also deliberate about when and howto make a commitment. Third, LVC require theagents to have information about the actual andalternative options of their opponents in order tobe able to calculate the Nash equilibrium decom-mitment threshold. This assumption is unrealisticin practical scenarios and is not required in ourmodel. Finally, unlike LVC (which typicallyassumes a fixed penalty for decommitting, regard-less of the stage of the process at which thecommitment is broken), our model takes the costof ongoing commitment into account by introduc-ing variable penalty contracts. Again, we believethis is more realistic for most real-world settings.

5. Conclusions and future work

This paper has introduced a commitmenthandling capability that can be applied in manag-ing concurrent negotiations in time-constrained


settings. This ability increases the flexibility andrealism of the participating sellers and relaxes theprevious unrealistic constraints we imposed [3,4].Our empirical results have highlighted the fact thatdifferent penalty levels have different effects on theperformance of the model. In addition, we showthat the more patient the buyer is, the better thedeal it will obtain. Nevertheless, if the buyer wantsto secure more agreements, it should be greedier inmaking commitments. Our extended model is alsocurrently being used in a number of real worldapplications to form and maintain coalitions inbusiness and e-science virtual organizations [22]and in an internal project of BT concerned withlogistics planning [23].

For the future, there are a number of ways inwhich our model can be improved. First, we wouldlike to experiment with different strategies (e.g.,alternative methods for the buyer to decidewhether or not to accept an offer from a seller)for our buyer agent to see how they affect the finaloutcome of the model. Second, we would like toinvestigate different penalty levels for differentagents, perhaps based on their negotiation histo-ries. In particular, if an agent comes to the negoti-ation with poor reputation (e.g., it frequentlyreneged on its previous encounters), that agentshould have to pay a higher penalty fee than onethat has shown itself to be more trustworthy.Finally, we would like to improve the decisionmaking of our agents so that they can make moreaccurate predictions about their opponents�decommitment strategies. This will, we believe,also increase the performance of the model.

References

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