Unanimously Acceptable Agreements for Negotiation Teams in Unpredictable Domains

Unanimously Acceptable Agreements for Negotiation Teams inUnpredictable Domains

Victor Sanchez-Anguixa, Reyhan Aydoganb, Vicente Juliana, Catholijn Jonkerb

aDepartamento de Sistemas Informaticos y ComputacionUniversitat Politecnica de Valencia

Camı de Vera s/n, 46022, Valencia, SpainbInteractive Intelligence GroupDelft University of Technology

Delft, The Netherlands

Abstract

A negotiation team is a set of agents with common and possibly also conflicting preferences that forms oneof the parties of a negotiation. A negotiation team is involved in two decision making processes simulta-neously, a negotiation with the opponents, and an intra-team process to decide on the moves to make inthe negotiation. This article focuses on negotiation team decision making for circumstances that requireunanimity of team decisions. Existing agent-based approaches only guarantee unanimity in teams negoti-ating in domains exclusively composed of predictable and compatible issues. This article presents a modelfor negotiation teams that guarantees unanimous team decisions in domains consisting of predictable andcompatible, and alsounpredictable issues. Moreover, the article explores the influence of using opponent, andteam member models in the proposing strategies that team members use. Experimental results show thatthe team benefits if team members employ Bayesian learning to model their teammates’ preferences.

Keywords: Automated negotiation, Multi-agent systems, Agreement technologies

1. Introduction

In the last decade, there has been an increasein the profit earned by electronic commerce sys-tems. This increase has lead to a strong interestof the academic world in researching problems re-lated to e-commerce (Ngai and Wat, 2002; Grieger,2003; Wareham et al., 2005). As of today, most e-commerce systems rely on users manually browsingtheir catalogs and selecting which goods they desireto buy. This task may end up being time consumingand suboptimal in terms of users’ preferences, es-pecially as the number of items and services offeredon the Web increases. Therefore, it is necessaryto propose mechanisms that helps costumers takebetter decisions while saving their time efforts.

Agent-based electronic commerce has been pro-posed as a solution to such problems (Guttman

Email addresses: [email protected] (VictorSanchez-Anguix), [email protected] (ReyhanAydogan), [email protected] (Vicente Julian),[email protected] (Catholijn Jonker)

et al., 1998; Sierra and Dignum, 2001; Oliveira andRocha, 2001; He et al., 2003). In an agent-based e-commerce system, autonomous agents act on behalfof their users with the goal of finding and closingsatisfactory deals. Automated negotiation is oneof the most common approaches when implement-ing these systems since they allow different elec-tronic parties to reach agreements by exchangingoffers and feedback (Lomuscio et al., 2003; Nguyenand Jennings, 2005; Buffett and Spencer, 2007; lau,2007; Chan et al., 2008). The benefits of automatednegotiation and agent-based e-commerce are many.Being brief, some of the most important include:

• As stated, browsing online catalogs for an op-timal deal may be time consuming. The state-of-the-art in automated negotiation can com-plete complex negotiations for multiple issuesin less than a few minutes (Klein et al., 2003a;Williams et al., 2011; Baarslag et al., 2012).

• On the one hand, automated negotiation savesthe user from having to browse the entire cata-

Preprint submitted to Elsevier May 17, 2014

log. Additionally, its personal agent is directedby the preferences of the user in the negotia-tion, which should result in deals that are ad-justed to the personal liking of the individual.Personalization has been reported to increaseuser satisfaction in many computational sys-tems (Ball et al., 2006; Liang et al., 2007). Onthe other hand, a dynamic process like auto-mated negotiation allows sellers to adapt theirdeals to the users’ preferences, their currentbusiness needs, and their competitor dynamics(He et al., 2003).

• Agreements achieved by human negotiators,suffer from the leaving money on the nego-tiation table effect (Thompson, 2003). Thismeans that human negotiators are contentwith current agreements, which are usuallysuboptimal, when they could have performedmuch better. Agents in automated negotiationhave been reported to provide agreements closeto the optimal solution (Lai et al., 2008).

• Compared to centralized and offline ap-proaches (e.g., preference aggregation, recom-mendation approaches, etc.), automated nego-tiation is a dynamic and parallel process. Forinstance, some centralized approaches like pref-erence aggregation are computationally hardespecially if the preference space is combina-torial (Chevaleyre et al., 2007). On the otherhand, recommendation approaches only filterprospective deals, but they do not close specificcontracts adapted to business needs. Contrar-ily, automated negotiation can be adapted tocurrent business needs (e.g., concede to gaincustomers and close fast deals). Additionally,as stated above, team members are also moti-vated by their own personal interests. There-fore, it is possible that some team membersshow opportunistic behavior inside the team.In such cases, preference aggregation may bemanipulated by exaggerating preferences. Ad-ditionally, each parties’ preferences are private,therefore making it difficult for the other par-ties to exploit and manipulate. This latter fac-tor is important, since nowadays most users inelectronic applications care about the informa-tion they filtrate in systems (Taylor, 2003).

Most negotiation mechanisms proposed for e-commerce settings have focused on solving bilat-eral or multiparty negotiations where parties are

individual agents (Faratin et al., 1998; Zeng andSycara, 1998; Klein et al., 2003b; Nguyen and Jen-nings, 2005; Coehoorn and Jennings, 2004; Buf-fett and Spencer, 2007; Lai et al., 2008; Williamset al., 2011; Sanchez-Anguix et al., 2013; Aydoganand Yolum, 2012). However, some real life scenar-ios involve negotiation parties that are not neces-sarily formed by single individuals. Instead, eachparty may be formed by more than a single individ-ual. For instance, imagine that a group of travelerswants to go on a holiday together. As a group, theyhave to negotiate with several travel agencies to getthe best travel package for the group. Despite shar-ing a common goal, each member in the multiplayerparty may also be motivated by its own personalinterests Mannix (2005); Halevy (2008). Therefore,the group not only faces a possibly difficult nego-tiation with the travel agency, but it also needs todeal with the conflict present in the group. Thistype of multi-individual negotiating party has beenstudied in the social sciences under the name of ne-gotiation team (Thompson et al., 1996; Brodt andThompson, 2001).

As far as the authors are concerned, multi-individual parties have been overlooked in auto-mated negotiation research. The use of computa-tional models for negotiation teams opens doors fornew types of interesting and novel applications inelectronic commerce. The inclusion of agent-basednegotiation teams allows for e-commerce systems todeploy dynamic deal mechanisms for groups, mak-ing of e-commerce a more social system. Classi-cally, when purchasing for groups in e-commercesystems, one representative takes decisions for thewhole group. Either he makes decisions accord-ing to his own preferences or the group needs toengage in a human negotiation which is usually acostly process due to different schedules, logistics,lack of communication problems or interpersonalconflict (Behfar et al., 2008). With the inclusionof agent-based negotiation teams these problemsare eluded since autonomous agents take decisionsjointly while saving time and efforts for their users.

We believe that agent-based negotiation teamscould provide potentially interesting new services :

• Electronic markets for groups of travelers:Online travel agencies offer their services bymeans of online catalogs where users canbrowse different products like flights, hotels,restaurants, activities, etc. The possibili-ties for travels are vast, and usually a single

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travel operator may offer thousands of possi-ble trip packages/services. Exhaustively look-ing through this online catalog for an optimaldeal becomes an unfeasible task for humans.Additionally, more often than not, travel is asocial activity for groups (e.g., friends, family,young people, etc.). Users can benefit fromagent-based negotiation teams since they canexhaustively look for deals while taking thepreferences of the group into account and sav-ing efforts. Service providers can also bene-fit from these models since they could adapttheir business strategies in a dynamic way andadd a level of personalization that may help toretain customers. Moreover, offering the pos-sibility for groups to close travel deals basedon their preferences is a value-added service,that as far as we know, is not currently of-fered by the industry. As an example of itsapplication, users may indicate to their per-sonal agents their desire to go on a travel to-gether. Then, the agents prepare to negotiatewith different travel agencies in order to pro-vide a complete and satisfactory travel packagefor the users. The fact that the negotiation iscarried out automatically by electronic agentsalso gives room to looking for several alterna-tives in parallel. Once several trip packageshave been negotiated, the personal agents maycommunicate the agreements to users, who canvalidate them in the last instance.

• Electronic support for agricultural coopera-tives: Agricultural cooperatives are supposedto be democratic institutions where groups offarmers join together to save resources for thedistribution of their products. One of the mainproblems of agricultural cooperatives is theprincipal-agent problem (Ortmann and King,2007). Basically, despite being democratic in-stitutions, agricultural cooperatives are man-aged by a board of directors who take deci-sions on behalf of the democratic institution.It has been reported in the literature (Ort-mann and King, 2007) that dissatisfaction incooperatives comes from the fact that the goalsof members are not aligned with those of themanagers. As a novel application for electroniccommerce, agent-based negotiation teams mayprovide support for the processes that are car-ried out by cooperatives. For instance, thenegotiations between agricultural cooperatives

and distributors may be supported by an elec-tronic market where the agricultural coopera-tive is modeled as an agent-based negotiationteam. Each member may be represented by anelectronic and personal agent that participatesin the negotiation team according to the pref-erences of its owner. This way, if the modelis capable of ensuring unanimity with regardsto team decisions, it may be possible to avoidthe principal-agent problem. Of course, agri-cultural cooperatives are large institutions andconsiderable research has still to be done toprovide scalable and fair computational mod-els. However, research as the one presented inthis article contributes to the obtention of suchmodels in the long term.

• Groups of energy producers in the smart grid:The smart grid is addressed to be the nextgeneration network for electricity distribution(Farhangi, 2010). In this network, energygeneration may come from geographically dis-tributed small generators (e.g., green energygenerators) that have to compete with largeenergy producers. Decisions at the smart gridhave to be taken dynamically since energy pro-duction and consumption may vary or face un-expected events (Ramchurn et al., 2012). Re-cently, agent-based electronic commerce hasbeen proposed as proper paradigm for this sce-nario due to its dynamic nature and adaptiveresponse (Brazier et al., 2002; Lamparter et al.,2010; Morais et al., 2012; Ramchurn et al.,2012). If small generators want to competewith large generators like power plants, theymay need to group together and act togetheras a single generator. Agent-based negotiationteams can give support for the group decisionmaking of small generators in a dynamic en-vironment like the smart grid. For instance,an agent-based negotiation team for the smartgrid may decide on different contract attributeslike energy price for different time slots, con-tract duration and cancellation fees with dif-ferent energy consumers.

The applications described above present benefitsfor electronic commerce systems. However, thereare still several issues that need to be solved for de-ploying real applications based on agent-based ne-gotiation teams due to the novelty of the topic. Oneof the main issues that should be addressed when

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designing agent-based negotiation team models isunanimity. The authors argue that, whenever it ispossible, it is desirable for the final agreement withthe opponent to be unanimously acceptable for allof the team members. When the members of thenegotiation team are going to interact in the longterm, the intra-team strategy should avoid one orsome of the team members being clearly at disad-vantage (e.g., unacceptable deal) with respect tothe other team members. In the first place, theaforementioned situation may end up in users per-ceiving unfairness, which may affect commitmentto the decision, group attachment, and trust (Ko-rsgaard et al., 1995). And second, but not the leastimportant, users that are not satisfied with agree-ments found automatically may end up leaving theelectronic commerce application.

The existing approaches (Sanchez-Anguix et al.,2011, 2012a,b) have focused on achieving unani-mously acceptable agreements for negotiation do-mains exclusively comprised by predictable andcompatible issues among the team members. Anissue is predictable and compatible if the preferenceorder over issue values is the same for team mem-bers and this fact is known from the domain (e.g.,price in a team of buyers). While some e-commercedomains are exclusively composed by these issues,many domains also contain issues whose preferen-tial ordering over issue values is not known from thedomain (i.e., unpredictable issues). For instance, itis difficult to predict from a set of cities which rank-ing represents the preferences of a traveler, whichcan diverge from the preferences of other travelers.

This article advances the state of the art in agent-based electronic commerce in two different ways.Firstly, it introduces a new model for agent-basednegotiation teams, which could support dynamicnegotiations for groups of autonomous agents rep-resenting their users. Secondly, the present modelis capable of assuring that the final agreement isunanimously acceptable for all of the team mem-bers in domains that contain both predictable andcompatible and unpredictable issues. We propose anintra-team protocol in which a team mediator helpsteam members to reach unanimously acceptable de-cisions. Furthermore, we propose two negotiationstrategies for team members: a basic negotiationstrategy based on concession tactics and a nego-tiation strategy using Bayesian learning to modelteammates’ and opponent’s preferences for unpre-dictable issues. The model is capable of outper-forming state-of-the-art approaches for agent-based

negotiation teams. We describe our general frame-work in Section 2 and the intra-team protocol thatallows team members to reach unanimity in Section3. After that, we propose two negotiation strategiesfor team members in Section 4 and we explain whyunanimity is guaranteed among team members inSection 5. After analyzing the experiments in Sec-tion 6, we relate our work to existing approachesand discuss future lines of work in Section 7.

2. Overview of the Negotiation Framework

Let A represent a negotiation team consisting of|A| = M different team members and a trustedteam mediator medA, and let a ∈ A represent ateam member in negotiation team A. Let op rep-resent the opponent party of the negotiation team.The negotiation between team and opponent is car-ried out in a bilateral fashion, using an alternating-offers protocol (Rubinstein, 1982). In this proto-col, one of the two parties is the initiating partyand sends the first offer to the other party or re-sponding party. The responding party receives theoffer and decides whether or not he/she accepts theoffer. Accordingly, she or he may accept the cur-rent offer or send a counter-offer. If the respondingagent sends a counter-offer, the initiating party hasto decide whether he/she accepts the counter-offeror not. If the counter-offer is rejected, the processis repeated in a turn-taking fashion until a deal ismutually accepted (successful negotiation) or oneof the parties decides to quit the negotiation sinceits deadline has been reached (failed negotiation).Concerning inter-party communications, the teammediator interacts with the opponent by sendingteam’s proposals and transmitting opponent deci-sions to team members. The team mediator plays akey role since it coordinates the team members andhelps them reach unanimously acceptable deals.

Let X be the object under negotiation, j ∈{1, ..., n} be the issues under negotiation, Dj be thenegotiation domain or valid values for issue j andxj ∈ Dj represent a valid value for issue j. Eachagent’s preferences are represented by means of aprivate additive utility function. We assume thatthere is no preferential interdependency among ne-gotiation issues; that is, the valuation given to acertain issue does not affect preference on the valua-tion of other negotiation issues. The utility functionfor an agent in our framework can be formalized as

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follows:

U(X) = w1V1(x1)+w2V2(x2)+...+wnVn(xn). (1)

where wj represents the importance given to issuej by the agent, and Vj : xj → [0, 1] is a scoringfunction for issue j that gives the score that theagent assigns to an issue value xj . It is assumed

thatn∑

j=1

wa,j = 1 and wa,j ≥ 0, and then U(.) is

a function scaled in [0,1], where 0 represents theleast desirable negotiation deals, and 1 representsthe most desirable negotiation deals. For agents,RU ∈ [0, 1] represents the reservation utility or theminimum level of utility to consider an agreementas acceptable.

In the proposed framework, private informationand bounded rationality are assumed. The formerhas been introduced above: information regardingagents’ preferences is private, and so are the strate-gies and minimum acceptable values of each agent.This is true even among team members, since priorto the negotiation they do not know any informa-tion regarding other teammates’ preferences. Theonly information available is obtained via interac-tions in the intra-team protocol. The latter refersto the fact that given the limited time, informa-tion privacy, and limited computational resources,agents cannot calculate the optimal strategy to becarried out during the negotiation. Instead, theyemploy heuristic strategies that aim to be as goodas possible in terms of the achievable utility.

2.1. Unanimously acceptable agreements

Each team member a ∈ A has a reservation util-ity RUa ∈ [0, 1] that represents the minimum util-ity that satisfies the team member’s need. Eachoutcome whose utility is lower than the reservationutility is unacceptable for the team member. Asstated along this article, we consider that unanim-ity in a negotiation team is of extreme importance.An offer is unanimously acceptable for a team A ifit is acceptable for all of the team members insidethe negotiation team:

∀a ∈ A,Ua(X) ≥ RUa. (2)

The proposed intra-team strategy will assurethat team members only accept those offers thatare unanimously acceptable for all the team mem-bers and that offers proposed to the opponent areover each team members’ reservation utilities, thus,making it unanimously acceptable.

2.2. Types of negotiation issues among team mem-bers

Among the different negotiation issues that com-pose the negotiation domain, we consider thatthere are issues that are predictable and compatibleamong team members and issues that are unpre-dictable among team members.

Formally, we can define an issue j with domainDj as compatible among team members if for eachpossible pair of team members a, b ∈ A and foreach pair of issue values v1, v2 ∈ Dj , the followingexpression is true:

Va,j(v2) > Va,j(v1)→ Vb,j(v2) ≥ Vb,j(v1). (3)

Hence, an issue is compatible among team membersif one of the team members can increase its utilityby selecting a certain issue value with respect tothe current assignment, then the rest of team mem-bers stay at the same utility or they also increasetheir utility. Thus, there is no preferential conflictamong issue values between the team members, andthere is full potential for cooperation among teammembers with respect to compatible issues. Figure1 shows two examples of compatible issues amongtwo agents (top part) and an example of a non com-patible issue (bottom part). As it can be observed,in the case of price (top left), both agents obtain abetter valuation when choosing a lower price valuewith respect to a high price value. Thus, Equation3 holds and it is a compatible issue for both agents.In the case of the city of destination (top right), theissue is also compatible among the two agents. Forany pair of cities, if one of the agents prefers one ofthe cities with respect to other city, the other agentalso holds the same preferential relationship. Forinstance, both agents prefer Paris to Berlin, Berlinto London, and London to Madrid. However, in thecase of the type of room (bottom part), the blueagent prefers an individual room with respect to anapartment, whereas the red agent prefers exactlythe opposite. Thus, there is no full potential for co-operation among team members in that negotiationissue since conflict is present.

The concept of predictability and unpredictabil-ity (Hindriks and Tykhonov, 2010; Marsa-Maestreet al., 2013) is related to vertical and horizon-tal issues found in economics literature (Stole,1995). The definition of predictable issues matcheswith vertical issues, while the definition of un-predictable issues matches with horizontal issues.From this point on, we will use the concepts of

5

10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

Price ($)

V(v

)

London Paris Madrid BerlinCity of destination

Individual Double Triple ApartmentType of room

Figure 1: Two compatible issues among two agents (top) and a non compatible issue among two agents (bottom).

unpredictable/predictable and we will briefly intro-duce them. An issue is predictable for an agent ifthe preference ordering of issue values is known inthe negotiation domain. Therefore, an issue is com-patible and predictable among team members if thepreferences regarding issue values are known in thenegotiation domain and increasing the utility of oneof the team members by selecting one specific issuevalue results in other team members staying at thesame utility or also increasing their respective util-ities. For instance, from the examples in Figure 1,one can consider that inside a team of buyers theprice is a compatible and predictable issue amongteam members since it is known that all of the buy-ers prefer low prices to high prices, and reducingthe price results in all of the buyers increasing theirutility or staying at the same utility. On the otherhand, an issue is unpredictable among team mem-bers if the preference ordering of the issue valuescannot be accurately predicted and Equation 3 maynot hold for that issue. In the case of Figure 1,the city of destination is a compatible issue amongthe two agents. Nevertheless, in a travel negotia-tion domain it is not true that all of the travelerswill hold the same preference ranking over the issue

values and without additional knowledge, the pref-erence ordering may not be predicted accurately.Hence, it is an unpredictable issue. With respectto the type of room, the preference ordering overissue values may vary for the travelers. Moreover,we cannot predict their preference ordering directly,thus making the issue unpredictable.

In this framework, PR denotes the set of pre-dictable and compatible issues among team mem-bers, while UN denotes the set of unpredictable is-sues.

2.3. Forbidden unpredictable partial offers amongteam members

We define an unpredictable partial offer X′

asa partial offer that has a concrete instantiationof all the unpredictable issues in UN. The utilityof an unpredictable partial offer is calculated asUa(X

′) =

∑j∈UN

wa,jVa,j(xj).

For a team member a ∈ A, an unpredictable par-tial offer X

′will never be part of an acceptable offer

(i.e., it will never be an unanimously acceptable of-fer for the team) when the sum of the utility of X

′

and the maximum utility that can be obtained from

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predictable issues maxPRa =∑

j∈PRwa,j is less than

its reservation value RUa, since any full offer thatcompletes X

′is below the reservation utility. For a

team member a, we refer to the set of unpredictablepartial offers that will never be part of an accept-able offer as forbidden unpredictable partial offers,Fa (see Equation 4).

Fa = {X′|Ua(X

′) +maxPRa < RUa} (4)

It is worth noting that Fa does not represent thewhole negotiation space that is unacceptable for a,but just a portion of it. In fact, some unpredictablepartial offers that are not contained in Fa, can be-come unacceptable when the agent does not get thevalue needed from predictable issues. The size of Fa

may grow as the reservation utility increases. Thus,agents with high reservation utilities are expectedto have larger sets of Fa than agents with low reser-vation utilities.

2.4. Case of Study

In this article we have employed a case of study(i.e., a negotiation domain) that is extracted froma possible tourism electronic market. The case ofstudy is used to illustrate and test the proposednegotiation framework.

A group of travelers wants to go on a holidaytogether and arrange their accommodation. Thegroup negotiates with a hotel on the following is-sues.

• Price (p): It represents the price per nightthat each traveler pays to the hotel for thebooking service. The value goes from 200$,which is the minimum rate applicable by thehotel, to 400$, which is the maximum ratefound in the hotel. This negotiation issue isconsidered to be predictable and compatibleamong team members since all of the travel-ers obviously prefer low prices to high prices.Contrarily, the hotel prefers high prices to lowprices.

• Cancellation fee (cf ): This issue representsthe amount of the final price that each friendpays if the reservation is canceled. Possiblevalues for this negotiation issue go from 0% to50%. This is a predictable and compatible is-sue among team members since all of the trav-elers prefer low cancellation fees to high can-cellation fees. On the contrary, the opponent

prefers high cancellation fees to low cancella-tion fees.

• Arranged Foods Included (af ): The hotelmay also offer some meals included in deal withthe travelers. The type of meal plans includedare none, breakfast, breakfast+lunch, break-fast+dinner, lunch+dinner, and all. In our ne-gotiation scenario, we have considered that thisnegotiation issue is unpredictable among teammembers since preferences of team members onthis issue may vary and it cannot be assumedto be same for each member.

• Type of room (tr): The four travelers canbe accommodated in different types of roomdepending on their preferences. More specif-ically, the hotel offers 4 individual rooms, 2twin rooms, 1 triple and 1 individual room, or1 apartment. The type of room is an unpre-dictable negotiation issue among team mem-bers.

• Payment method (pm): The amount ofmoney paid by the travelers may be paid bydifferent methods. The hotel allows for thepayment to be made in cash, via credit card,by bank transfer, in a 3 months deferred pay-ment through the bank, and in a 6 months de-ferred payment. This negotiation issue is un-predictable since team members may prefer tochoose different payment methods and we can-not predict their preference ordering directly.

• Room orientation (ro): If possible, the teammembers can decide upon an orientation forthe balcony of their rooms. The different op-tions are inner garden, main street, pool, sea,and outer garden. This issue is also consideredan unpredictable issue among team members.

• Free amenity (fa): As a token of generos-ity for booking as a group, the hotel offers onefree service to all of the team members. Morespecifically, the team members can choose be-tween gym service, free wi-fi, 1 free drink perday, 1 free spa session, pool service, cable tvservice, and one free guided tour. Since thepreferences of team members vary for this is-sue and no assumption about their preferencescan be made, this issue is also considered asunpredictable.

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To sum up, for this case study we have thatPR= {p,cf } and UN = {af ,tr ,pm,ro,fa} with a to-tal of 4200 different combinations of discrete issuevalues (af,tr,pm,ro,fa) and two real issues (p,cf ).We assume that the team mediator knows which is-sues are predictable and can apply an operator thatdetermines the best value for team members from agiven set. For unpredictable issues, team memberscan have different types of valuation functions andthe mediator does not know which issue values arebetter for team members. Each team member mayassign different weights (i.e., priorities) to negotia-tion issues and the opponent’s valuation functionsand issue weights may be different from those ofteam members. The team mediator does not knowthe weights given by agents to the different issues.

3. Intra-Team Protocol

In a negotiation involving a negotiation team,the intra-team protocol defines how and when de-cisions are taken regarding the negotiation. In thisframework, we propose an intra-team protocol thatis governed by the trusted team mediator medA.Basically, the team mediator regulates the interac-tions that can be carried out among team mem-bers and, accordingly, helps team members reach-ing unanimous acceptable decisions inside the teamduring the negotiation. The proposed protocol isclearly differentiated into two different phases: Pre-negotiation and Negotiation. On the one hand, dur-ing the pre-negotiation, the mediator helps teammembers identifying potential offers that are notunanimously acceptable for every teammate. Onthe other hand, during the negotiation the mediatorcoordinates the offer proposal mechanism, which iscomposed of a voting process for unpredictable is-sues and an iterated building process for predictableissues, and the offer acceptance mechanism for of-fers that come from the opponent. We describethose phases in a detailed way in the following sec-tions 3.1 and 3.2. An overview of all of the com-munications carried out in the negotiation modelare depicted in Figure 2. It specifies the protocolscarried out within the team and the communica-tions carried out with the opponent by means ofAgent UML (Bauer et al., 2001) sequence diagrams.More detailed views of the intra-team protocols forthe pre-negotiation, evaluation opponent’s propos-als and proposing offers can be observed in Figures3, 4, and 5 respectively.

3.1. Pre-negotiation Phase

In the pre-negotiation phase, the mediator co-ordinates the following intra-team protocol to dis-cover the set of forbidden unpredictable partial of-fers FA for the team . The set of forbidden unpre-dictable partial offers for the team, FA, is definedas FA = {X ′|∃a ∈ A,X ′ ∈ Fa}. This means thatany unpredictable partial offer in FA is never partof an acceptable offer for at least one team mem-ber. Thus, these unpredictable partial offers shouldbe avoided for the team since the goal of the nego-tiation model is reaching unanimously acceptableagreements.

A formal description of the pre-negotiation pro-tocol is presented in Figure 3. The picture describesthe protocol by means of Agent UML sequence di-agrams. According to the proposed protocol, theteam mediator initiates the pre-negotiation phaseby asking each team member a to calculate itsown set of forbidden unpredictable partial offers Fa

(message 1 in Figure 3). Each team member buildsits own (forbidden) set as requested, and it is com-municated to the mediator privately (message 2 inFigure 3). When the mediator receives the sets fromthe team members, it aggregates them in order toconstruct the set of forbidden unpredictable partialoffers for team A, FA =

⋃a∈A

Fa. Then, the team

mediator makes public the list of forbidden unpre-dictable partial offers of the team FA (message 3in Figure 3). It should be stated that, since anyunpredictable partial offer in this set will preventone of the team members from reaching its reser-vation utility, the team is not allowed to generatean offer involving any of these partial offers in FA.After the team mediator has shared FA with teammembers, the negotiation phase starts.

The reader may realize that it is possible thatduring this phase, most of the unpredictable par-tial offers are pruned. In that case, it means thatthere is little potential for cooperation among teammembers. This issue can be observed by the teammediator prior to starting any negotiation process.In that case, the team mediator may suggest theteam not to negotiate and save the computationalresources used in the negotiation. If the team isnot static and can be dynamically formed, it maysuggest team members to disband the team andlook for other potential partners. However, thisteam/coalition formation(Gaston and desJardins,2005; Rahwan et al., 2009) is outside of the scopeof this work since we focus on studying the perfor-

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Team Mediator Team Member aOpponent op

1. INFORM Start negotiation

ref Pre-negotiation

2. INFORM Start negotiation

3. ACK

[deadline] 4.a INFORM withdraw

ref Offer proposal

5. PROPOSE

[deadline]6.a INFORM withdraw

[acceptable] 6.b ACCEPT

6.c PROPOSE6.b.1 INFORM Accept

[deadline]7.a INFORM withdraw

ref Opponent’s Offer Evaluation [acceptable] 8.a ACCEPT

t

AX

t

opX

Figure 2: Overview of the communications carried out by the team mediator.

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Team Member aTeam Mediator1. REQUEST

2. INFORM

3. INFORMA

F

aF

SD Pre-negotiation

aF

Figure 3: Overview of the intra-team protocol carried out during the pre-negotiation

mance of the negotiation model. We consider theuse of the information provided with forbidden un-predictable partial offers for negotiation team for-mation as a future line of work. In general, combi-nations of team members that prune a small portionof the space should be more similar among them,and it should be more easy to achieve cooperation.

3.2. Negotiation Phase

In the negotiation, two mechanisms are carriedout at each round: a mechanism for deciding to ac-cept/reject the opponent’s offer (Evaluation of Op-ponent’s Offer), and a mechanism for proposing anoffer to the opponent (Offer Proposal). For the for-mer, a unanimity voting process is employed, whilefor the latter an offer building process is governedby the team mediator.

3.2.1. Evaluation of Opponent’s Offer

This mechanism is carried out each time the teammediator receives an offer from the opponent. Sincethe main goal of the proposed intra-team strategyis achieving unanimously acceptable agreements forthe team, a unanimity voting is carried out to de-cide whether or not the opponent’s offer is accept-able for the team. With this mechanism, as longas one of the team members is not satisfied withthe opponent’s offer, the offer is not accepted bythe team, precluding the team from reaching agree-ments that are not unanimously acceptable. A for-malization of the protocol followed in this mech-anism can be observed in Figure 4. The pictureshows the formalization employing sequence dia-grams from Agent UML. The intra-team protocolused for this mechanism goes as follows. First, theteam mediator receives the offer Xt from the op-ponent at time t. If Xt involves any forbidden un-predictable partial offer in FA, the opponent offer

is automatically rejected. However, the opponent’soffer is also informed to team members in order toallow each team member to process the new infor-mation leaked by the opponent if they see it nec-essary (message 1 in Figure 4). Otherwise, if thecombination of unpredictable issue values is not inFA, in order to see whether the offer is unanimouslyacceptable for team members, the mediator makesthe opponent’s offer public among team membersand starts an anonymous voting process (message2 in Figure 4). Each team member a ∈ A statesto the mediator whether he is willing to accept Xt

(positive vote) or to reject it (negative vote) at thatspecific instant (messages 3.a or 3.b in Figure 4).Since our aim is to guarantee unanimity, the offeris only accepted if all of the team members emit apositive vote (message 4.a in Figure 4). Otherwise,the offer is rejected and a counter-offer is proposedas explained in Section 3.2.2.

3.2.2. Offer Proposal

Proposing an offer to the opponent is a complextask, since the space of offers may be huge and thepreferences of the team members should be reflectedin the offer sent to the opponent, and, in our case,the offer sent should be unanimously acceptable forteam members. The process is divided into twosub-phases: constructing an unpredictable partialoffer, and setting up predictable issues. In bothphases, the team mediator acts according to Algo-rithm 3.1. We include another formal description ofthe interactions between the mediator and a teammember during the offer proposal. This informa-tion can be found in Figure 5, which depicts theintra-team protocol specified in and Agent UMLsequence diagram.

• Constructing an unpredictable partialoffer: The first step is to propose an un-

10

Team Mediator

2. REQUEST accept opponent offer ?t

opX

Team Member a

t

opX

SD Evaluation of Opponent’s Offer

3.a ACCEPT

3.b REJECT

4.a INFORM ACCEPT

4.b INFORM REJECTt

opX

])([A

t

opFXUN

1. INFORMt

opX

Figure 4: Overview of the intra-team protocol employed to evaluate opponent’s offers.

predictable partial offer, a partial offer whichhas all of the unpredictable issues instantiated.Since team members know from FA the list ofunpredictable partial offers that will not re-sult in unanimously acceptable offers underany circumstance, any offer proposed by theteam should avoid being constructed from un-predictable partial offers found in FA. Themethod used to propose offers to the oppo-nent relies on the fact that unpredictable is-sues are those where intra-team conflict maybe present, whereas there is full potential forcooperation in predictable and compatible is-sues. Hence, in order to build an offer to besent to the opponent, it seems more appro-priate to jointly set unpredictable issue val-ues first and then, depending on the remainingneeds of team members, allow team membersto set compatible and predictable issues as theyrequire for reaching their demands. The pro-posed mechanism for the first part, proposingan unpredictable partial offer, is based on vot-ing and social choice. The voting process goesas follows.

1. The mediator asks each team member toanonymously propose one unpredictablepartial offer X

′ta (message 1 in Figure 5).

2. Each team member privately sends itsproposal to the mediator, who gathersall of the proposals in a list that will belater sent to team members. If any un-

predictable partial offer proposed by a iscontained in FA, the mediator automati-cally ignores this proposal (message 2 inFigure 5).

3. Once all of the proposals have been gath-ered, the mediator makes public the list

of proposal UPO′t among team mem-

bers and opens a Borda scoring process(Nurmi, 2010) on proposed candidates(message 3 in Figure 5).

4. Each team member anonymously scorescandidates and sends the scores to theteam mediator (message 4 in Figure 5).

5. The team mediator sums up scores and se-lects the winner candidate with the high-est score X

′tA , making it public among

team members (message 5 in Figure 5).This candidate, an unpredictable partialoffer, will be the base for the full offer thatwill be sent to the opponent.

• Setting up predictable and compatibleissue values: Once unpredictable issues havebeen set, it is necessary to set predictable andcompatible issues to construct a complete offer.As it has been stated along this article, thereis full potential for cooperation among teammembers in these issues since increasing theutility of one of the team members by select-ing one issue value will result in the other teammembers staying at the same utility or increas-

11

ing their utility. Obviously, the selected unpre-dictable partial offer will not satisfy equallythe needs of all the team members. Never-theless, team members can make use of pre-dictable and compatible issues to satisfy theirremaining needs while not generating conflictinside the team. To complete the partial offerX

′tA , an iterative mechanism that we proposed

in (Sanchez-Anguix et al., 2012a) is used tobuild the final offer issue per issue. The mecha-nism follows an order for predictable and com-patible issues that is constructed by the me-diator at each round according to the historyof the opponent’s concessions. The rationaleused to build this order is that the opponentwould concede less on those predictable issuesmore important for him in the first negotia-tion rounds, whereas it would concede moreon those predictable issues that are less impor-tant. Thus, the order established by the teammediator attempts to order predictable andcompatible issues in ascending order of impor-tance for the opponent. The general idea be-hind this ordering is attempting to satisfy teammembers’ demands with those predictable is-sues less important for the opponent first. Theorder is updated as new information becomesavailable from the offers sent by the opponent.Based on this order, the iterative mechanismgoes as follows.

6. The mediator selects the first predictableissue j and asks team members, given thecurrent partial offer X

′tA , the necessary

value xj for j to get as close as possibleto their current demands (message 6 inFigure 5).

7. Accordingly, each team member a informsthe mediator privately about the mostconvenient value xa,j for that issue (mes-sage 7 in Figure 5). To decide the finalvalue xj for the issue j, the trusted media-tor aggregates agents’ opinions (since theissue is predictable) by means of a func-tion that, for team members, returns themost preferred issue value from a givenset (best(.)). After deciding the value xj ,

X′tA is updated with xj .

8. The mediator asks the team whether ornot the new partial offer is already satis-factory at round t (message 8 in Figure

5).

9. Each team member emits an affirmativeresponse if the current partial offer cov-ers its current demands and a negativeresponse if it still has not covered its de-mands (message 9.a or 9.b in Figure 5).Those agents that agree with the currentstate of X

′tA leave the iterative mechanism

for this offer since they already are satis-fied with the current partial offer. Theprocess steps back to the selection of thenext issue.

10. The process continues until all of the pre-dictable issues have been set or until allof the team members have left the it-erative mechanism. In the latter case,the remaining issues are set attemptingto maximize the opponent’s preferences.Once the offer is complete, it is announcedamong team members and sent to the op-ponent (message 10.b in Figure 5).

Algorithm 3.1. Pseudo-algorithm for the offerconstruction from the point of view of the medi-ator. Send (message −→ condition ) means thatmessage is sent to every agent that fulfills condi-tion

1:

2: /*Proposing an unpredictable offer*/3: Send (REQUEST X

′ta −→ ∀a ∈ A)

4: Receive (INFORM X′ta ←− ∀a ∈ A)

5: UPO′t = (

⋃a∈A

X′ta )− FA

6: Send (REQUEST Borda on UPO′t −→ ∀a ∈

A)7: Receive (INFORM scorea ←− ∀a ∈ A)8: X

′tA = argmax

X′∈UPO′t

∑a∈A

score(a,X ′)

9: Send (INFORM X′tA ←− ∀a ∈ A)

10: order = build predictable order(); A′ = A11:

12: /*Setting predictable issues*/13: for all j ∈ order do14: Send (REQUEST value for j −→ ∀a|a ∈ A′)15: Receive (INFORM xa,j ←− ∀a|a ∈ A′)16: xj = best({xa,j |a ∈ A′})17: X

′tA = X

′tA

⋃{xj}

18: Send (REQUEST Satisfied with X′tA? −→

∀a ∈ A′)19: for all a ∈ A′ do20: Receive (INFORM ac′a(X

′tA) ←− a)

12

21: if ac′a(X′tA) = true then

22: A′ = A′ − {a}23: end if24: end for25: if A′ = ∅ then26: break;27: end if28: end for29: for all j ∈ order ∧ issue not set(j) do30: xj = maximize for opponent(j)

31: X′tA = X

′tA

⋃{xj}

32: end for33: Xt

A = X′tA

4. Team Members’ Strategies

The team mediator defines the coordinationmechanisms inside the team. However, each teammember’s internal strategy has a great effect onteam dynamics. In this article, we propose twotypes of strategy for team members. Accordingto the first strategy (i.e., our basic team member),the team member only proposes unpredictable par-tial offers based on its own utility. In the secondstrategy, team members model the preferences ofthe team and the opponent on unpredictable par-tial offers. Then, in the mechanism employed toset unpredictable partial offers, each team memberselects the candidate that guarantees that it canreach its current aspirations at time t, and max-imizes the probability of being acceptable for theopponent and the team. The learning mechanismemployed by these team members is Bayesian learn-ing (i.e., Bayesian team member).

4.1. Basic Strategy for Team Members

Since negotiations are time-bounded in ourframework, we consider that team members haveto perform some kind of concession if an agreementis to be found. For this purpose we have designedbasic team members as agents whose demands arecontrolled by an individual and private concessionstrategy. More specifically, the concession strategyfor a team member a ∈ A is based on time-basedtactics sa(t) (Faratin et al., 1998; Lai et al., 2008).It estimates the utility demanded by a at time tby using the formula in Equation 5, where RUa isits reservation utility, T is the negotiation deadline,and βa is the concession speed, which determineshow fast the agent’s demands are lowered towardsRUa.

sa(t) = 1− (1−RUa)× (t

T)

1βa (5)

Based on this concession tactic, each team mem-ber participates in the intra-team protocol withtheir demands regulated by his private concessiontactic. Next, we define how team members taketheir decisions: evaluating the opponent’s offer, andproposing an offer for the opponent.

4.1.1. Evaluation of Opponent’s Offer

Given an offer Xt proposed by the opponent atinstant t, the team member emits a positive vote inthe unanimity voting process if it reports a utilitygreater than or equal to its current demands sa(t).Otherwise, a negative vote is emitted.

aca(Xt) =

{true if sa(t) ≤ Ua(Xt)false otherwise

(6)


As documented in Section 3.2, team membersinteract at three points during the offer proposal.First, they propose an unpredictable partial offerto the team mediator. Since each team member ahas its demands regulated by a time-based tactic,when proposing an unpredictable partial offer to themediator at instant t, the proposed unpredictablepartial offer X

′ta fulfills:

X′ta /∈ FA ∧ (Ua(X

′ta ) +maxPRa ≥ sa(t)) (7)

Hence, agent a selects an unpredictable partialoffer which is not forbidden inside the team (sinceit will be ignored by the team mediator) and whoseutility allows him to achieve or surpass its currentdemands at time t. This way, the team member as-sures that if its proposed unpredictable partial offeris the winner of the Borda voting process, it canreach its current demands. However, one should beaware that many unpredictable partial offers mayfulfill Equation 7. Therefore, it is necessary to se-lect one of them as the proposed candidate. Beingour basic team member, from the set of partial of-fers that fulfill Equation 7, a team member selectsone of the candidates randomly.

The second time that a team member interactswith the team mediator is for scoring unpredictablepartial offers that have been proposed by teammembers. For scoring candidate partial offers in

13

Team Mediator

1. REQUEST unpredictable partial offer

2. INFORM

Team Member a

t

aX

'

3. REQUEST Borda on

4. INFORM

5. INFORM winner unpredictable partial offer

ascore

t

AX

'

6. REQUEST value for issue j

7. INFORMt

jax

,

8. REQUEST Satisfied with ?

t

aX

'

},...,{''

1

' t

M

ttXXUPO

SD Offer Proposal

9.a INFORM OK

9.b INFORM NO

[All issues instantiated] 10. b INFORMt

AX

10.a REQUEST value for next issue j

}{''' t

j

t

A

t

AxXX

SD Unpredictable Issues

SD Predictable and Compatible Issues

Figure 5: Overview of the intra-team protocol carried out to propose offers to the other party.

14

the Borda voting process, a basic team member or-ders the candidates according to the partial utilityreported by each of the candidates. That is, theteam member assigns the highest score to the par-tial offer whose utility is the highest for itself, andthe second highest score to the partial offer whoseutility is the second best one, and so forth.

Finally, team members also interact with the me-diator during the mechanism used to set predictableand compatible issues. When team members areasked about a value for issue j, each team mem-ber communicates anonymously the value xa,j . Thevalue is the one that, given the current partial offerX

′tA , gets the utility of the new partial offer as close

as possible to its current aspiration sa(t). Takingnormalized additive utility functions, it can be cal-culated as:

xa,j =

argmax Va,j(x)

x∈Djif Ua(X

′tA) + wa,j ≤ sa(t)

argmin Va,j(x)x ∈ Dj∧wa,jVa,j(x) ≥ (sa(t)− Ua(X

′tA ))

otherwise

(8)where sa(t) is the utility demanded by the agenta at round t, Ua(X

′tA) is the utility reported by

the current partial offer, and wa,jVa,j(x) is theweighted utility reported by the value demandedby the agent. The value asked for issue j is theclosest one to the current demands of the agent.On the one hand, if the agent cannot reach its cur-rent demands by just setting issue j, it asks for thevalue that reports the highest utility. On the otherhand, if the agent can reach or surpass its currentdemands by setting j, it asks for the value thatmakes the new partial offer the closest to the cur-rent demands. In the same iterative process, teammembers still have to declare whether or not theyare satisfied with the different partial offers that areconstructed. Team members follow a similar crite-rion to the method proposed to determine if an op-ponent offer is acceptable at t. Basically, a partialoffer is acceptable for an agent a at t if it reports autility greater than or equal to the aspiration levelmarked by its concession strategy:

ac′a(X′tA) =

{true if Ua(X

′tA) ≥ sa(t)

false otherwise(9)

where true indicates that the partial offer is ac-ceptable at its current state for agent a, and falseindicates the opposite.

4.2. Bayesian-based Strategy for Team Members

The Bayesian-based negotiation strategy for ateam member is based on modeling the team’s (asa whole) and its opponent’s preferences on unpre-dictable issues, and acting accordingly. For thispurpose, two Bayesian models are employed to pre-dict if unpredictable partial offers are acceptablefor both teammates and the opponent. One of theBayesian models is employed to capture the prefer-ences of the team on unpredictable issues, whereasthe other is used for capturing the preferences ofthe opponent on unpredictable issues. The strategyused to evaluate the opponent’s offer is the same asthe one described in the basic strategy.

4.2.1. Bayesian Learning

Bayesian learning is a probabilistic learningmethod based on Bayes’ theorem (Russell andNorvig, 2003). Given a certain set of hypothesisH and some observation e, Bayesian learning at-tempts to compute the probability p(h|e) that acertain hypothesis h is true after observing e. In ourcase, we want to determine whether or not the pro-posed offer will be acceptable for the opponent (orthe team) (H={acc,¬acc}) given a certain unpre-dictable partial offer (e = X

′t) where acc stands for“acceptable” and ¬acc stands for “unacceptable”.

Since we assume that there is no interdependenceamong negotiation issues, we can consider that eachnegotiation issue contributes individually to the ac-ceptability of an offer/unpredictable partial offer.Thus, applying Bayes’ theorem under independenceassumption we have:

p(acc|X′t) =

p(acc)∏

j∈UNp(xj |acc)∑

H∈{acc,¬acc}p(H)

∏j∈UN

p(xj |H)(10)

where p(acc) is the prior probability for an unpre-dictable partial offer to be acceptable, p(¬acc) isthe prior probability for an unpredictable partial of-fer to be non-acceptable, and p(xj |acc) is the condi-

tional probability that assuming X′t as acceptable,

it has the value of the j issues instantiated to xj .

We consider positive examples Sacc as those ex-amples that correspond to the acceptable hypothe-sis (acc) and negative examples S¬acc as those ex-amples that correspond to the not acceptable hy-pothesis (¬acc). For the opponent’s model, we em-ploy unpredictable partial offers that have appeared

15

in opponent’s offers as positive examples, and un-predictable partial offers that appear in offers re-jected by the opponent as negative samples. Forthe team’s model, we use FA and those opponent’soffers rejected by team members as the set of neg-ative examples. Winners in the Borda votings (i.e.,unpredictable partial offers contained in offers sentto the opponent) are considered as positive exam-ples. For computing p(xj |h), we use the proportionbetween the number of times that xj appears inhypothesis h (acc or ¬acc) and the total number ofexamples for h:

p(xj |h) =#{xj ∈ Sh}|Sh|

(11)

The reasons for employing Bayesian learning arevaried. The most important one is that it allowsonline updating of the model as new samples be-come available. This is important in a processlike negotiation, where at each interaction new in-formation becomes available regarding the oppo-nent’s/teammates’ preferences. If a computation-ally expensive learning mechanism was used, itwould not be possible to include the new informa-tion in the model as it becomes available. Further-more, the learning mechanism is computationallycheap since it mainly involves counting. This isalso important in a real application since it allowsfor simultaneous negotiation threads to exist, whichshould be maintained with different opponents tolook for the best alternatives in an electronic mar-ketplace.


Bayesian models are employed to help in the se-lection of the unpredictable partial offer that is pro-posed to the other team members. Bayesian teammembers propose at t unpredictable partial offersin the set defined in Equation 7. Bayesian modelshelp to select a candidate from that set.

However, it is reasonable to think that in the firstinteractions Bayesian model do not accurately rep-resent other agents’ preferences. For that purpose,a team member invests part of the negotiation timetexp in exploring the negotiation space and collect-ing information regarding the opponent’s and theteam’s preferences. As long as the negotiation pro-cess has not surpassed texp, the team member justselects randomly one of candidate unpredictablepartial offers as basic team members do. Mean-while, the Bayesian models are continuously up-

dated with the new information that becomes avail-able during the negotiation. After reaching the timethreshold, the team member starts to use Bayesianmodels in order to select the unpredictable partialoffer to be proposed to the mediator during the offerproposal phase. The heuristic used in the selectionof the candidate is proposing an unpredictable par-tial offer that is both acceptable for the team andthe opponent. The model has an additional pa-rameter named pesc. It represents the probabilityof avoiding the Bayesian proposal model and usingthe random proposal model as described in the ba-sic team member model when the negotiation timehas gone beyond texp. This parameter is includedin the model in order to: (i) further explore thenegotiation space; (ii) escape from local optima in-duced by inaccurate Bayesian models (e.g., wrongsamples, limited number of samples, etc.). We canformalize the selection as follows:

X′ta =

argmaxX∈B

∑wbpb(acc|X)b∈{A,op}

if

rand ≤ pesc∧t ≥ texp

random partial offer(B) otherwise(12)

where B is the set of candidate unpredictable par-tial offers that fulfill Equation 7, rand is a randomnumber, pA(acc|X) is the probability for a candi-date unpredictable partial offer to be acceptablefor the team, popp(acc|X) is the probability for thecandidate unpredictable partial offer to be accept-able for the opponent, and wA and wop

1 representthe weights given to the acceptability of the un-predictable partial offer for the team and the op-ponent, respectively (i.e., we will refer to them asBayesian weights). Varying these Bayesian weightsallow team members to show different behaviors de-pending on their inclination to satisfy either theteam or the opponent with the unpredictable par-tial offer.

5. Provably Unanimously Acceptable Deci-sions

As stated in the introduction, one of our re-search goals is proposing a negotiation team modelthat is able to guarantee unanimously acceptableteam decisions. Next, we show that under the as-

1wA + wop = 1.

16

sumption of rationality2, team members are able toachieve unanimously acceptable final agreements, ifan agreement is found. For that matter, let us em-ploy reductio ad absurdum (reduction to absurdity).

If X is the final agreement, let us suppose thatEquation 2 (unanimously acceptable) is violated ina negotiation: unanimity is not reached because aobtained a utility below its reservation utility.

∃a ∈ A,Ua(X′t) +

∑j∈PR

wa,jVa,j(xj) < RUa (13)

The final agreement is found when (1) team mem-bers accept an opponent’s offer or (2) the opponentaccepts a team’s offer. Next, we show that in bothcases, Equation 13 is never true.

1. When the team members accept an opponent’soffer, a unanimity voting process has been car-ried to decide whether or not to accept the finaloffer. The offer is only accepted if all of theteam members have emitted a positive vote.Since a rational agent a would never have in-centive to emit a positive vote of the offer re-ported a utility below its reservation utility,this scenario is never true due to the intra-teammechanism.

2. When the opponent accepts a team’s offer X,this offer has been necessarily proposed bythe intra-team mechanism mentioned in Sec-tion 3.2.2. The offer can be decomposed intoan unpredictable partial offer X

′t and the in-stantiation of predictable issues. The teammember a is not able to get over its reserva-tion utility if and only if X

′t ∈ Fa or whenX

′t /∈ Fa and a could not get what it de-manded in predictable issues. A rational agenthas no incentive to exclude a forbidden unpre-dictable partial offer X

′t when declaring Fa.Since FA =

⋃a∈A

Fa and the mediator ignores

unpredictable partial offers in FA, an unpre-dictable partial offer X

′t that forms a teamoffer is never in Fa. If X

′t /∈ Fa then theagent can accomplish to satisfy the followingexpression Ua(X

′t) +maxPRa ≥ RUa. Agenta could not get over its reservation value be-cause he could not demand the most of pre-dictable issues. However, when the team me-diator aggregates predictable issues inside the

2Rational agents seek to improve their current welfare.Thus, they would not take actions that lead to utilities belowtheir reservation utilities.

team, the team mediator selects the highestvalue for team members in the list of valuesproposed by them. This makes possible for a toobtain the maximum utility from predictableissues. Hence, Equation 13 never holds if thenegotiation ends with agreement.

Since both possible scenarios are never true un-der our initial assumption, we have shown by re-duction ad absurdum that, if a final agreement isfound, it is unanimously acceptable among teammembers. Another issue is the presence of exagger-ating agents (i.e., agents that exaggerate to get themost from the negotiation). In our setting, even ifteam members exaggerate and decide to include inFa unpredictable partial offers that are acceptablebut report low utility, or demand more than theyneed from predictable issues, if a final agreement isfound it will be unanimous among team members.However, by doing so, they may be pruning negoti-ation space and lowering the probability of findingagreements. This is an interesting situation that weplan to study in the future.

6. Experiments

In this section, we explore the behavior of theproposed negotiation model in different scenar-ios. The proposed framework has been imple-mented in genius (Lin et al., 2012), a simulationframework for automated negotiation that allowsresearchers to test their frameworks and strate-gies against state-of-the-art agents designed byother researchers. Recently, genius has become awidespread tool that increases its repository of ne-gotiating agents with the annual negotiation com-petition (Baarslag et al., 2012).

In order to assess the performance of the pro-posed negotiation approach, we have performed dif-ferent experiments. All of the experiments havebeen carried out in the negotiation domain (or casestudy) introduced in Section 2.4. The first exper-iment (Section 6.1) studies the performance of theproposed model when facing single opponent agent.The comparison is carried out in scenarios with dif-ferent degrees of team’s preference dissimilarity. Inthe second experiment, we study the performanceof our negotiation team model when facing anothernegotiation team in bilateral negotiations. In thethird experiment (Section 6.3) we study how theBayesian weights wA and wop, which control theimportance given to the preferences of the team and

17

the opponent in the unpredictable partial offer pro-posed to teammates, impact the performance of theproposed model when team members employ theBayesian strategy. Finally, we conduct an experi-ment to study the effect of team members’ reser-vation utility on the performance of the proposednegotiation model (Section 6.4).

6.1. Performance Against a Single Opponent

In this first set of experiments we study the per-formance of the proposed negotiation team modelwhen facing a single opponent. The study is carriedout with an emphasis on observing if the perfor-mance of the team is higher by employing Bayesianteam members rather than basic team members.Due to the fact that we are interested in open en-vironments, we study how the team performancevaries with team configurations ranging from sce-narios where no team members plays the Bayesianstrategy (i.e., all Basic team members) to situa-tions where all the team members play the Bayesianstrategy. The performance of the team is measuredusing the average team joint utility3. As an addi-tional measure of optimality, we also measure thedistance to the closest Pareto optimal point. In thiscase, the Pareto frontier is computed taking into ac-count the team joint utility and the utility of theopponent. Our initial hypotheses were:

• H1 As more Bayesian team members form theteam, the team is able to obtain average teamjoint utilities that are higher than or equal tothose configurations with less Bayesian teammembers.

• H2 As more Bayesian team members form theteam, the team is able to obtain average oppo-nent utilities that are higher than or equal tothose configurations with less Bayesian teammembers.

Since Bayesian team members take the prefer-ences of the team and the opponent into accountwhen deciding which offer is sent to the other part,they should be able guarantee equal or higher av-erage team joint utility and opponent utility thanbasic team members. But in no case, they should

3We consider the joint utility of the team to be the prod-uct of the utilities of the team members. Since the utility ofan agent is between 0 and 1, the team joint utility tends tobe lower as more team members are present.

not obtain lower team joint utility and opponentutility. As a consequence of both hypothesis, thedistance to the closest Pareto optimal point shouldbe also equal or lower than that obtained by config-urations solely composed by basic team members.

In order to compare the proposed model withother models in the literature, we also includedthe Similarity Borda Voting model (i.e., SBV)(Sanchez-Anguix et al., 2011) in our experiment.SBV is a mediated intra-team strategy that is ableto guarantee semi-unanimity regarding team deci-sions. The mediator imposes a unanimity votingprocess to decide on whether or not to accept theopponent’s offer, whilst team members propose of-fers to be sent to the opponent by means of a simi-larity heuristic that takes into account the last offerproposed by the opponent, and the last offer pro-posed by the team. A Borda voting process is usedin order to decide on which offer is sent to the oppo-nent. The reason to include this intra-team strat-egy in our study is due to the fact that it has beendocumented to achieve similar results to intra-teamstrategies that guarantee unanimity under certaincircumstances for domains solely composed by pre-dictable issues (Sanchez-Anguix et al., 2011). Inorder to adapt this approach for domains with un-predictable issues, we use a similarity heuristic thatuses Euclidean distance for real/integer issues andstring matching for other types of issues. Due tothe fact that our proposed model guarantees unan-imously acceptable agreements and SBV does not,we formulated the following hypothesis:

• H3 Teams exclusively formed by basic teammembers and teams exclusively formed byBayesian team members obtain equal or higheraverage team joint utility than teams followingthe Similarity Borda Voting model.

The performance of this first experiment is an-alyzed in three scenarios with different degrees ofpreference dissimilarity among team members: verysimilar, average similarity, and very dissimilar pref-erences. For this reason, we introduce a measurefor measuring team members’ preference similar-ity in different scenarios. The authors proposed amethod for calculating preference dissimilarity inteams based on the utility difference of offers amongteammates (Sanchez-Anguix et al., 2011). The dis-similarity between two teammates a, b ∈ A can be

18

measured as:

D(Ua(.), Ub(.)) =

∑∀X|Ua(X)− Ub(X)|

# possible offers(14)

Due to the fact that a team may be composedof more than two members, it is necessary to pro-vide a team dissimilarity measure. The team dis-similarity measure is calculated as the average ofthe dissimilarity between all of the possible pairs ofteammates. For this experiment, we decided to ex-plore teams whose preferences are dissimilar, teamswhose preferences are similar, and teams with anaverage degree of similarity/dissimilarity (i.e., aver-age similarity). For the scenario of dissimilar prefer-ences, 9 negotiation cases were randomly generated(i.e., a combination of 3 different negotiation teamsconsisting of four team members with 3 different op-ponents), while 9 negotiation cases were randomlygenerated for the similar preferences scenario (i.e.,a combination of 3 different negotiation teams con-sisting of four team members with 3 different op-ponents) and 12 negotiation cases were randomlygenerated for the average similarity scenario (i.e.,a combination of 4 different negotiation teams con-sisting of four team members with 3 different op-ponents). Since we consider that in practice it isless likely to meet extreme cases such as dissimilaror similar teams, we decided to increase the num-ber of negotiation cases in the average similarityscenario.

As for the single opponents, we decided to testthe negotiation team models against different fami-lies of opponents. More specifically, we followed thecategorization of negotiation strategies proposed byBaarslag et al. (Baarslag et al., 2011), which di-vides negotiation strategies into four categories:

• Competitors: They hardly concede, indepen-dently of opponent behavior. Agent K isa competitor agent (Kawaguchi et al., 2011;Baarslag et al., 2011) from the 2010 ANACcompetition(Baarslag et al., 2012) that adjustsits aspirations (i.e., target utility) in the nego-tiation process considering to an estimation ofthe maximum utility that will be offered by theother party. More specifically, the agent grad-ually reduces its target utility based on the av-erage utility offered by the opponent and itsstandard deviation.

• Matchers: They concede when they perceivethat the opponent concedes, and they do not

concede if they perceive that the other partydoes concede. Nice Tit-for-Tat is a matcheragent (Baarslag et al., 2011, 2013) from the2011 ANAC competition that reciprocates theother party’s moves by means of a Bayesianmodel of the other party’s preferences. Accord-ing to the Bayesian model, the Nice Tit-for-Tatagent attempts to calculate the Nash point andit reciprocates moves by calculating the dis-tance of the last opponent offer to the afore-mentioned point. When the negotiation timeis reaching its deadline, the Nice TFT agentwill wait for an offer that is not expected toimprove in the remaining time and accept it inorder to secure an agreement.

• Conceders: They yield independently of theopponent behavior. Conceder is an imple-mentation of the time-based concession tacticsproposed by Faratin et al. (Faratin et al., 1998)categorized by Baarslag et al. as conceder. Forthe Conceder agent βop = 2, which leads tolarge concessions towards the reservation util-ity in the first rounds.

• Inverter: They respond by implementing theopposite behavior shown by the other party.Boulware is an implementation of the time-based concession tactics proposed by Faratinet al. (Faratin et al., 1998) categorized byBaarslag et al. as inverter. In the case ofthe Boulware agent, the concession speed is setto βop = 0.2. Hence, the agent concedes veryinsignificantly during most of the negotiationand it concedes very quickly as the deadlineapproaches.

The reservation utility of each team member wasset to RUa = 0.5 to represent scenarios where teammembers have average aspirations. Additionally,for each team member (i.e., basic, Bayesian andSBV) the concession speed was randomly selectedfrom a uniform distribution βa = U [0.5, 1]. Inthe case of Bayesian members, the time of explo-ration was set to texp = 70% and the probabilityof escape after the exploration phase was set topesc = 30% 4. Therefore, Bayesian models are notused unless a 70% of the negotiation time (126 sec-onds) has passed. Initially, we set Bayesian mem-

4These values were found to be the best ones after carry-ing out a grid search over values of texp and pesc in a subsetof test negotiation scenarios

19

SimilarAgent K Nice Tit-for-Tat Boulware Conceder

T. Op. D. T. Op. D. T. Op. D. T. Op. DSBV 0.181 0.743 0.070 0.150 0.694 0.130 0.184 0.755 0.064 0.552 0.482 0.037Basic 0.259 0.683 0.065 0.173 0.760 0.067 0.223 0.696 0.078 0.561 0.468 0.045

Bayesian 0.263 0.690 0.058 0.164 0.746 0.080 0.224 0.695 0.080 0.557 0.472 0.043Average Similarity

Agent K Nice Tit-for-Tat Boulware ConcederT. J Op. D. T. J Op. D. T. J Op. D. T. J Op. D.

SBV 0.168 0.629 0.065 0.137 0.562 0.116 0.170 0.598 0.070 0.324 0.428 0.074Basic 0.211 0.574 0.070 0.141 0.691 0.050 0.210 0.585 0.060 0.386 0.414 0.052

Bayesian 0.248 0.583 0.034 0.158 0.669 0.047 0.224 0.574 0.045 0.390 0.414 0.050Dissimilar

Agent K Nice Tit-for-Tat Boulware ConcederT. J Op. D. T. J Op. D. T. J Op. D. T. J Op. D.

SBV 0.07 0.522 0.168 0.160 0.457 0.157 0.128 0.547 0.110 0.257 0.430 0.110Basic 0.174 0.397 0.180 0.184 0.572 0.055 0.254 0.505 0.053 0.472 0.367 0.046

Bayesian 0.209 0.457 0.118 0.196 0.559 0.60 0.271 0.489 0.058 0.475 0.367 0.044

Table 1: Average team joint utility (T. ), the average opponent utility (Op.), and the average Euclidean distance to the closestPareto optimal point (D.) for the first set of experiments.

bers to care equally about the acceptability of un-predictable partial for the team and the opponentwA = wop = 0.5.

Following the type of setting used in the annualagent competition, the negotiation time was set toT = 180 seconds. Each opponent strategy wasfaced against each negotiation team model in ev-ery possible negotiation case. A total of 20 repe-titions were done per negotiation case in order tocapture stochastic variations in negotiation strate-gies. Therefore, 3 × 3 × 3 × 4 × 20 = 2160 (teampreference profiles × opponent preference profiles ×team negotiation models × opponent strategies ×repetitions) negotiations were simulated in the sim-ilar scenario, 2160 negotiations were simulated inthe dissimilar scenario, and 2880 negotiations weresimulated in the average similarity scenario.

Table 1 shows the average team joint utilityand opponent utility for the cases where all of theteam members either play the Basic strategy, theBayesian model, or the team employs the SBV teamnegotiation model. It also shows the Euclidean dis-tance to the closest point in the Pareto frontier. AnANOVA test (α = 0.05) with a Bonferroni post-hoc analysis was carried out to assess statisticaldifferences among the different measures gathered.Those measures that are statistically the best con-figurations for each column are highlighted in boldstyle. All of the claims in this experimental sec-tion are supported by the ANOVA test with theBonferroni post-hoc analysis. The average negotia-

tion time taken by each method is included in Ta-ble 2. Figure 7 shows the evolution of the averageteam joint utility and the average opponent utilityas more team members play the Bayesian strategy.We have also included some examples of agreementsobtained in the different negotiation scenarios andhow they relate to the Pareto frontier5. These re-sults can be observed in Figure 6. Next, we analyzethe results.

6.1.1. Results for the first hypothesis

• H1 As more Bayesian team members form theteam, the team is able to obtain average teamjoint utilities that are higher than or equal tothose configurations with less Bayesian teammembers.

First, we focus on the situations when all of theteam members either play the basic strategy or theBayesian strategy (Tables 1 and 2). It can be ob-served that when team members’ preferences aresimilar, both types of teams perform equally interms of the average team joint utility. This resultis consistent with H1, since both prove to be statis-tically equivalent with the ANOVA test with Bon-ferroni post-hoc analysis. The reason why Bayesian

5The quadratic root of the team joint utility is taken toconvert the results to the same scale (remember that theteam joint utility is the product of for team members’ utili-ties)

20

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Figure 6: Examples of agreements and their distance to the Pareto frontier

21

models do not give an advantage over the basicmodel in the similar scenario can be explained sinceteam members are similar and there is no neces-sity to carry out team modeling. The distance tothe closest Pareto optimal point is also very simi-lar for both team configurations, which can be alsoexplained due to the fact that team modeling isnot necessary due to team members’ similar prefer-ences.

As conflict is introduced inside the team by mak-ing team members’ preferences more dissimilar (i.e.,dissimilar and average similarity scenarios, middleand bottom part of Table 1), it can be observed thatusually the team formed exclusively by Bayesianteam members gets the statistically highest averageteam joint utility, which is also coherent with ourhypothesis H1 and refines our hypothesis for thesescenarios. In this case, the teammates’ preferencesare no longer similar and some sort of modelingmechanism is needed in order to guide the intra-team negotiation towards agreements that are goodfor all of the team members. The only exception isfound in the conceder case, where the performancein terms of the team joint utility was found to bestatistically equivalent among the team exclusivelyformed by basic team members and the team ex-clusively formed by Bayesian members. Taking acloser look at the negotiation traces, we observedthat, in all of the negotiations, the exploration timetexp was never surpassed. Since the Conceder agentconcedes rapidly in the negotiation, the team’s de-mands are also met early. Therefore, Bayesian mod-els do not get to be used. In fact, the average nego-tiation time against Conceder agents was 61.7, 76.3,and 88 seconds respectively in the similar scenario(see Table 2), the average similarity scenario (seeTable 2), and the dissimilar scenario (see Table 2).All of them are below the threshold of 126 secondsdelimited by texp. As a result, the team membershave not used their Bayesian model while generat-ing their proposals and they are equivalent to theteam formed by basic members. This is also con-sistent with H1, since in no case the team formedby Bayesian members gets statistically lower resultsthan the team formed by basic members.

If we observe the evolution of the average teamjoint utility in Figure 7 6, there is a tendencyto increase the average team joint utility as moreBayesian members are included (triangle shaped

6Results for the Conceder agent are omitted since theBayesian models are not employed.

SimilarK N. TFT B. C.

SBV 148.7 164.3 139.4 61.0Basic 141.5 162.5 145.4 62.8Bayesian 142.3 165.2 144.0 61.7

Average SimilarityK N. TFT B. C.


DissimilarK N. TFT B. C.


Table 2: Average time (seconds) for negotiations in the firstset of experiments. K (Agent K), N. TFT (Nice Tit-for-Tat),B. (Boulware), C. (Conceder)

data series on Figure 7) in situations where teammembers’ preferences have an average similarity orthey are very dissimilar. This tendency is morepronounced against Agent K (left plot in Figure7) and Boulware agents (right plot in Figure 7).However, when team members’ preferences are verysimilar the team performance remains at statisti-cally equivalent values (ANOVA test with Bonfer-roni analysis) for the average team joint utility. Theresults of these graphics are coherent with our find-ings in Table 1 and H1.

In conclusion, we have found that as moreBayesian team members form the team, the team isable to obtain average team joint utilities that arehigher than or equal to those configurations withless Bayesian team members. Being more specific,we have been able to detect that, as long as thereis preferential conflict among team members (i.e.,average similarity among team members, and verydissimilar team members), and the opponent doesnot concede early in the negotiation, more Bayesianteam members result in higher team joint utility.

6.1.2. Results for the second hypothesis

• H2 As more Bayesian team members form theteam, the team is able to obtain average oppo-nent utilities that are higher than or equal tothose configurations with less Bayesian teammembers.

For the average opponent utility, the Bayesianteam obtained significantly better results than thebasic team only in the scenario where the team faces

22

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Figure 7: Evolution of the average team joint utility and opponent utility as more Bayesian team members are introduced inthe team.

Agent K and team members are dissimilar withregards to their preferences (see Table 1, bottompart). The same pattern is found in Figure 7, wherewe can observe that the average opponent utility in-creases as more Bayesian team members are presentin the team (first plot in the second row of Figure7). In other cases, the Bayesian and the basic teamobtain statistically equivalent results to each other,and, in some situations, the basic team obtainedsignificantly better results. More specifically, whenthe team faces Nice Tit-for-Tat, the basic team ob-tains significantly better results than the Bayesianteam. We can also observe this pattern in Figure7. As more Bayesian members are introduced, theaverage opponent utility slightly decreases (middleplot in the second row of Figure 7).

These findings only support partially our hypoth-esis H2 since we found a set of scenarios where thebasic team provides better utility to the opponent(i.e., when facing Nice Tit-for-Tat). We analyzed

the trace of different negotiations against Nice Tit-for-Tat and Boulware opponents. In the formercase, we could observe that close to the end ofthe negotiation the Nice Tit-for-Tat opponent hadonly sent on average 5 different unpredictable par-tial offers in a domain that has 4200 different un-predictable partial offers. This behavior results inscarce information for any learning mechanism. Inthe case of negotiations against Boulware agents,one should consider that the Boulware strategiesconcede only towards the end of the negotiationand, most of the time, the aspirations are high.Thus, most of the samples gathered by the Bayesianclassifier when facing Boulware agents correspondto offers with high demands where usually only thebest issue values appear. Other issue values do notappear in the samples or they have their frequencymisinterpreted with respect to the utility that theyactually report. Therefore, the learning mechanismmisinterprets the preferences of the opponent and

23

the team formed by Bayesian members is not ableto obtain statistically better utility for the oppo-nent than the team formed by basic members.

The behavior of Nice Tit-for-Tat and Boulwareopponents also has a direct consequence on the dis-tance to the closest Pareto optimal point obtainedby both team configurations (Bayesian and basic).Despite the fact that the Bayesian configuration iscapable of obtaining statistically better results forthe team joint utility by learning the preferencesof the team, the utility reported to the opponentis usually lower than the one reported by the ba-sic configuration. The only exception to this caseare scenarios against Agent K, where the Bayesianconfiguration obtains a statistically higher utilityfor the opponent. The inability to model the oppo-nents’ preferences in the case of the Boulware andNice Tit-for-Tat opponents, results in a higher teamjoint utility (due to team modeling) at the costof reducing the utility received by the opponent.Hence, there is not an improvement in the distanceto the closest Pareto optimal point. These find-ings can also be observed in some of the examplesincluded in Figure 6.The agreements found by thebasic team configuration and the Bayesian configu-ration tend to be found at the same distance to thePareto frontier (the Bayesian configuration tendingto populate regions with higher team joint utility).The exception to this rule are negotiations againstAgent K, where the basic configuration tends topopulate regions of no agreement (close to the axisorigin).

6.1.3. Results for the third hypothesis

• H3 Teams exclusively formed by basic teammembers and teams exclusively formed byBayesian team members obtain equal or higheraverage team joint utility than teams followingthe Similarity Borda Voting model.

It can be observed that when team members’ pref-erences are similar (top part of Table 1), both basicand Bayesian models are statistically equivalent toeach other and better than SBV with respect to theaverage team joint utility. As conflict is introducedinside the team by making team members’ prefer-ences more dissimilar (i.e., dissimilar and averagesimilarity scenarios, middle and bottom part of Ta-ble 1), the team get statistically lower average teamjoint utility by employing the SBV model. Basicand Bayesian models outperform SBV with respectto the average team joint utility since they are able

to guarantee unanimously acceptable agreements,while SBV does not guarantee such condition. Thisresult supports and refines our hypothesis H3, since,in general, the team formed exclusively by Bayesianteam members and the team formed by basic teammembers obtains statistically higher team joint util-ities than the SBV model. There is only one ex-ception to this refinement. The basic team, theBayesian team and SBV perform statistically equalin terms of the average team joint utility only whenthe opponent is a conceder and team members’ pref-erences are similar. Since the opponent concedesrapidly in the first rounds, the three models ob-tain equivalent team joint utility due to the oppo-nent concessions and the fact that conflict is almostnonexistent among team members. However, thisfinding is still consistent with our initial guess H3.

Regarding the optimality of the solutions foundby the model proposed in this article with respectto SBV, it is possible to observe that both Bayesianand basic configurations obtains statistically lowerdistance to the Pareto frontier than SBV as longas preferential conflict between team members ispresent (i.e., average similarity and dissimilar sce-narios). Only when the team is very similar, SBVgets statistically equal distances to the model pro-posed in this article. However, despite the fact thatthe distance to the Pareto frontier may be statisti-cally equal, we can observe in Figure 6 that agree-ments found by SBV tend to populate areas thatare closer to the lowest team joint utility. This re-sult can be explained due to the fact that unanimitycannot be guaranteed in the team, and some teammembers end up with low utility agreements.

In conclusion, we found that teams exclusivelyformed by basic team members and teams exclu-sively formed by Bayesian team members obtainequal or higher average team joint utility thanteams following the Similarity Borda Voting model.More specifically, we found that, in general, the re-sults for the team formed by Bayesian team mem-bers and the team formed by basic team membersobtains statistically higher results than the SBVmodel. The distance to the Pareto frontier alsoshows higher quality and more optimal agreementsfor teams employing the model proposed in thisarticle. This result is important, since it showsthat the present model, not only guarantees unan-imously acceptable agreements, but it also ensuresthat better results are obtained with respect toother state-of-the-art team negotiation models.

24

6.2. Performance Against Another TeamIn this experiment we analyze the performance

of the proposed model when two teams face eachother. More specifically, we simulate negotiationswhere one negotiation team represents a group offour travelers, and the other negotiation team rep-resents the board of managers for a hotel, whichconsists also of four managers. The negotiation hasa common deadline of T = 180 seconds. Both par-ties negotiate with each other by means of the al-ternating bilateral protocol, but they employ thenegotiation team model proposed in this article tocoordinate and take team decisions. The goal of theexperiment is determining if Bayesian team mem-ber improve the performance of the team when itfaces another team.

In this setting, we use 4 different team prefer-ence profiles to represent the group of travelers and2 different team preference profiles to represent theboard of managers. Since we are interested in openenvironments, we consider different team configura-tions from the perspective of strategy profiles: Noteam member plays the Bayesian strategy (0-0),halfof the team members play the Bayesian strategyin one team (2-0), all of the team members playthe Bayesian strategy in one team (4-0), half of theteam members are Bayesian in both teams (2-2), allof the team members are Bayesian in one team andhalf of them are Bayesian in the other team (4-2),and all of the team members are Bayesian (4-4).For each strategy profile, each group of travelers’ isfaced against each board of managers 20 times tocapture stochastic variations. Therefore, a total of4×2×20 = 160 negotiations is carried out per teamstrategy profile, giving a total of 960 negotiationsfor this experiment.

Our initial guess is that more Bayesian teammembers will help to obtain higher team joint util-ities due to the learning and proposal mechanismused to take into account the preferences of theteam and the preferences of the opponent. Morespecifically, we formulated the following hypothe-ses:

• H4 As long as only one team includes Bayesianteam members (configurations 2-0 and 4-0),the average team joint utility for both teamswill be higher than the average team joint util-ity obtained by negotiations where no Bayesianteam member participates (configuration 0-0).

• H5 Those configurations where both teams in-clude Bayesian team members (configurations

2-2, 4-2, and 4-4) will obtain higher aver-age team joint utilities for both teams thanconfigurations where only one team includesBayesian team members (configurations 2-0and 4-0).

We configure the parameters as we did in ourprevious experiment. The results of the experimentcan be observed in Figure 8. The blue points repre-sent the average team joint utility for the group oftravelers, whereas the red points represent the av-erage team joint utility for the board of managers.The graphic shows an increasing average team jointutility as the total of Bayesian team members inboth sides increases. The worst results for bothteams are obtained when all of the team membersact as the basic team member (0-0). This resultis explainable due to the large number of negoti-ations that finished with no agreement (80 out of160 negotiations, a 50% of failure). As long as oneof the sides implements the Bayesian strategy (2-0,4-0), both teams benefit by obtaining higher av-erage team joint utilities. An ANOVA test withBonferroni post-hoc analysis (α = 0.05) confirmedthat both configurations 2-0 and 4-0 obtain statis-tically different and higher team joint utilities forboth teams than the configuration 0-0. This resultconfirmed our initial hypothesis H4.

It can be observed that the next relevant increasein the average team joint utility of both teams ispresent as long as both sides apply the Bayesianstrategy (2-2, 4-2, 4-4). An ANOVA test with Bon-ferroni post-hoc analysis (α = 0.05) revealed thatthe averages obtained by configurations 2-2, 4-2,and 4-4 are statistically different and higher thanthe averages obtained by 2-0 and 4-0. Hence, bothteams obtain higher average team joint utilities aslong as both teams include Bayesian team members,supporting our hypothesis H5.

In conclusion, we have been able to determinethat when two teams face each other by means ofthe proposed model, both teams benefit by obtain-ing higher team joint utilities when Bayesian teammembers participate in the negotiation. This isespecially true when Bayesian team members aredistributed between both teams, which obtains thehighest team joint utilities for both sides.

6.3. Analyzing the impact of Bayesian weights forthe proposal of unpredictable partial offers

Recalling from Section 4.2, there are two weightparameters that control how important the op-

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ponent’s and team’s preferences are while gener-ating the unpredictable partial offer (respectivelywop, wA). wA represents how important it is forthe team members to make an unpredictable par-tial offer that is acceptable for the team, whereaswop represents how important it is for us to makean unpredictable partial offer that is acceptable forthe opponent. The use of these weights is not triv-ial, since one should consider that, it only refersto the acceptability of the unpredictable partial of-fer by one of the two parties. A complete offer iscomposed by the predictable and unpredictable is-sues. Therefore, for instance, using a high value ofwop may not have the desired effect on the oppo-nent unless unpredictable issues are important forthe opponent. Additionally, one should also con-sider that the more acceptable an unpredictable isfor the team/opponent, the more utility it shouldreport.

In this experiment we explore the impact of theseweights in a wide variety of situations. More specif-ically, we study how different values for wop and wA

affect situations where the team gives more impor-tance to unpredictable issues than the opponent,situations where the opponent gives more impor-tance to unpredictable issues than the team, andsituations where both team and the opponent givethe same importance to unpredictable issues.

To assess the importance given by an agent tounpredictable partial issues, we consider the sum ofunpredictable issue weights in its utility function.

Ia =∑

j∈UN

wi,j (15)

We consider that when Ia ∈ [0.0, 0.33] the agent agives low importance to unpredictable issues, when

Ia ∈ [0.33, 0.66] it gives average importance tounpredictable issues, and when Ia ∈ [0.66, 1.0] theagent gives high importance to unpredictable issues.We generated 8 random negotiation cases whereteam members give a high importance to unpre-dictable issues and the opponent gives low (4 cases)and average (4 cases) importance to unpredictableissues, 8 different randomly generated negotiationcases where team members give a low importanceto unpredictable issues and the opponent gives av-erage (4 cases) and high (4 cases) importance to un-predictable issues, and 12 negotiation cases wherethe opponent and the team give the same impor-tance to unpredictable issues (4 cases where bothgive low importance, 4 cases where both give aver-age importance, and 4 cases where both give highimportance).

We tested three configurations for Bayesianteams: standard Bayesian members that give thesame importance to the acceptability of the un-predictable partial offer by the opponent and theteam wA = wop = 0.5 (Normal), Bayesian mem-bers that give more importance to the acceptabil-ity of the unpredictable partial offer by the oppo-nent wA = 0.25 wop = 0.75 (Opponent Oriented),and Bayesian members that give more importanceto the acceptability of the unpredictable partial of-fer by the team wA = 0.75 wop = 0.25 (TeamOriented). As for the opponent’s strategies, we se-lected Agent K, Nice TFT and Boulware.

In situations where the opponent gives more im-portance to unpredictable issues than the team, theteam should be able to obtain higher average teamjoint utility by playing high values for wop, satisfy-ing opponent needs with unpredictable issues, anddemanding more on predictable issues. If the teamgives more importance to unpredictable issues, theteam should be able to obtain higher average teamjoint utility by playing high values for wA, satis-fying opponent needs with predictable issues, anddemanding more on unpredictable issues. If bothteams give the same importance to unpredictableissues, the team should be able to guarantee higheraverage team joint utility by giving the same weightto wop and wA since no party gives more importanceto unpredictable issues. Attending to these initialguesses, we formulated the following hypotheses:

• H6 When the opponent gives more impor-tance to unpredictable issues, the team obtainshigher team joint utility by using high valuesfor wop and demanding more on predictable is-

26

sues (wA = 0.25 wop = 0.75).

• H7 When the team gives more importance tounpredictable issues, the team obtains higherteam joint utility by using high values forwA and letting the opponent demand on pre-dictable issues (wA = 0.75 wop = 0.25).

• H8 When both parties give the same impor-tance to unpredictable issues, the team obtainshigher team joint utility by giving the sameimportance to the opponent’s and team’s pref-erences on unpredictable issues (wA = wop =0.5).

For each negotiation case, we repeated the nego-tiation 20 times in order to capture stochastic vari-ations in strategies. Therefore, a total of 1680 ne-gotiations were carried out in this experiment. Theresults of this experiment can be observed in Table3. It shows the average of the joint team utility andproportion of negotiations that finished with suc-cess (agreement) in the scenario. An ANOVA test(α = 0.05) with Bonferroni post-hoc analysis wascarried out to detect statistically different averages.The best configurations for each of the three sce-narios are highlighted in bold font style. All of theclaims of this experimental section are supportedwith the aforementioned ANOVA test with post-hoc analysis.

Focusing on the case of negotiations againstAgent K, it can be appreciated that when unpre-dictable issues are more important for the oppo-nent (bottom part of Table 3), the best resultsare obtained by taking an opponent oriented ap-proach: proposing unpredictable partial offers thatare likely to be acceptable for the opponent and sat-isfy remaining members’ aspirations by demandingon predictable and compatible issues, which are lessimportant for the opponent. This finding supportsH6. As for the scenario where unpredictable is-sues are more important for the team (middle partof Table 3), it is clearly observed that the bestchoice for team joint utility is to give a high weightto wA, thus employing a team oriented approach.Since unpredictable issues are more important forthe team, they should satisfy their needs as muchas possible with proposed unpredictable partial of-fers and demand less on predictable issues, whichare more important for the opponent, supportingour initial hypothesis H7. Finally, the last sce-nario corresponds to the case where unpredictableissues have the same importance for both parties

(top part of Table 3). In this case, there may bemore conflict between the team and its opponentsince the parties do not have a clear trade-off op-portunity such as increasing the demand on unpre-dictable issue while decreasing the demand on pre-dictable issues as appeared in two previous cases.One can observe that the best team joint utility isobtained when using the standard team members(wA = wop = 0.5). Since both parties give the sameimportance to unpredictable issues, it seems naturalto give the same importance to the acceptability ofthe unpredictable partial offer by the team and theopponent, supporting our hypothesis H8. The teamoriented approach is clearly worse than the rest ofapproaches since many negotiations (only a 58.7%were successful. See top part of Table 3 ) ended infailure due to the team being too demanding andnot satisfying the opponent’s preferences.

When negotiating against Nice TFT and Boul-ware, the results are different. It can be appreciatedthat, generally, the team oriented approach alwaysreports statistically better results from the point ofview of the average team joint utility. This meansthat the team should indistinctly select highly ac-ceptable unpredictable partial offers for the teamwhen facing opponents like Nice TFT and Boul-ware agents. These findings do not support ourhypotheses H6, H7, and H8, and drove a more in-depth analysis and study. There are two factorsthat should be taken into account. First, as we de-tected in Section 6.1, the Bayesian models that arelearnt from both agents are not adequate due tothe lack of learning samples detected in the case ofNice TFT and the misinterpretation of the impor-tance of issue values in the case of the Boulwareagent. This factor precludes the agents from find-ing good agreements for both parties when using anopponent oriented approach in scenarios where un-predictable issues are more important for the oppo-nent. Since the Bayesian models misinterpret thepreferences of Boulware and Nice TFT agents, itis not possible to create win-win situations. Sec-ond, by selecting a team oriented approach, theBayesian team members are selecting the more ac-ceptable (i.e., the best) unpredictable partial offersfor the team. These unpredictable partial offers re-port high utility for the team. Thus, once com-pleted with predictable issues, these offers are ex-pected to report high utility for the team. Differ-ently to Agent K, Nice TFT and Boulware agentsare not competitor agents since they will eventu-ally accept the team’s offer when the deadline is

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approaching. In the case of the Boulware agent, itconcedes quickly with respect to its aspirations asthe deadline approaches, eventually meeting the re-quirements of the demanding team offer. As statedin (Baarslag et al., 2013), when the negotiation timeis reaching its deadline, the Nice TFT agent willwait for an offer that is not expected to improvein the remaining time in order to secure an agree-ment. Hence, the team is able to exploit the otherparty by selecting the team oriented approach. Dueto these circumstances, hypotheses H6, H7, and H8were not supported for agents Boulware and NiceTit-for-Tat.

In conclusion, hypotheses H6, H7 and H7 are onlypartially supported. In general, we have discov-ered that depending on the type of opponent agent,the values for weights wop, wA have different effectson the negotiation. When facing exploitable agentslike Nice TFT and Boulware, the team benefits ifthe team members take the team oriented approach,selecting those unpredictable partial offers that aremore acceptable for the team. If the team facescompetitors like Agent K, the team should matchthe values for wop and wA depending on the impor-tance given by each party to unpredictable issues.It is acknowledged that, depending on the opponentand the desired behavior, the team should select dif-ferent values for the Bayesian proposal weights. Amechanism for adjusting Bayesian weights based onthe type of opponent is considered as future work.

6.4. Analyzing the Impact of the Reservation Util-ity

In this experiment, we investigated the impactof the reservation utility of team members on theteam joint utility. As explained in Section 3.1,team members jointly prune a part of the negotia-tion space (i.e., a set of unpredictable partial offers)which does not contain, with absolute certainty, anyunanimously acceptable offer. This pruning is re-lated with the reservation utility of team members,which represents the minimum acceptable utilityby team members. Any offer with a utility lowerthan the reservation utility is not acceptable for theagent.

Lower reservation utilities make it easier to ob-tain the needed utility by just setting compatibleand predictable issues. Thus, each team memberneeds to prune less negotiation space with the un-predictable partial offers sent to the team media-tor. Presumably, a joint list of forbidden unpre-dictable partial offers (i.e., the negotiation space

Similar Avg. Similarity DissimilarRUa = 0.35 0.4% 11.6% 35.3%RUa = 0.50 23.8% 34.2% 72.6%RUa = 0.65 73.7% 81.8% 90.8%

Table 4: Average percentage of unpredictable partial offerspruned in the pre-negotiation.

that is pruned) with lower reservation utilities issmaller than lists constructed with higher reserva-tion utilities. This leaves more room for findingan agreement with the opponent. However, if teammembers have low reservation utilities, despite hav-ing more room for finding an agreement, they mayend up with low utility agreements in the end. Onthe contrary, with higher reservation utilities, it isharder to obtain the needed utility with compat-ible and predictable issues. Therefore, each teammember may need to prune more negotiation spaceand the joint list of forbidden unpredictable partialoffers will be larger than the list constructed withlower reservation utilities. In fact, if team membersset high aspirations with their reservation utility,it may end up with all the negotiation space be-ing pruned. If an agreement is found under theseconditions, it may lead to team members achievinghigh levels of utility.

In this experiment, we test the impact of differentlevels of reservation utility on the team joint utility.More specifically, as we did in Section 6.1, we testedteams employing the Bayesian model against dif-ferent families of strategies: competitor (i.e., AgentK), matcher (i.e., Nice Tit-for-Tat), inverter (i.e.,Boulware), and conceder (i.e., conceder). As an ad-ditional dimension to our study, we also introducedpreference similarity among team members. There-fore, teams are tested in the scenario where teammembers’ preferences are dissimilar, the scenariowhere team members’ preferences have an averagedegree of similarity, and the scenario where teammembers’ preferences are similar.

We configured three types of Bayesian teams withdifferent levels of reservation utilities: a team witha relatively low reservation utility RUa = 0.35, ateam with a moderate reservation utility RUa =0.5, and a team with a high reservation utilityRUa = 0.65. We expect that playing higher reser-vation utilities against competitor like Agent K willresult in lower average team joint utility due tomany negotiations ending with no agreement. Onthe other hand, we expected that playing high reser-vation utilities against Conceder agents, inverter

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Equal importance on unpredictable issuesvs. Agent K vs. Nice TFT vs. Boulware

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.Normal 0.168 84.2 0.137 100 0.202 100

Opponent Oriented 0.155 91.1 0.126 100 0.188 100Team Oriented 0.116 58.7 0.188 100 0.206 100

Unpredictable issues more important for the teamvs. Agent K vs. Nice TFT vs. Boulware

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.Normal 0.213 100 0.135 100 0.185 100

Opponent Oriented 0.200 100 0.154 100 0.189 100Team Oriented 0.248 100 0.196 100 0.213 100

Unpredictable issues more important for the opponentvs. Agent K vs. Nice TFT vs. Boulware

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.Normal 0.280 100 0.186 100 0.326 100

Opponent Oriented 0.296 100 0.192 100 0.300 100Team Oriented 0.271 92.0 0.259 100 0.340 100

Table 3: Impact of wA and wop on the average team joint utility in different scenarios and proportion of negotiations thatfinished with success (% Ag.).

agents like Boulware, and the special case of NiceTit-for-Tat, would result in higher average teamjoint utility due to the fact that both agents shouldeventually concede towards the other parties’ de-mands. In the case of Nice Tit-for-Tat, we haveobserved that when the deadline is approaching itattempts to secure a deal, making this agent can-didate to be exploited by setting a high reservationutility. Therefore, we formulated the following hy-potheses:

• H9 Playing a high reservation value for teammembers (RUa = 0.65) will result in the lowestaverage team joint utility against Agent K.

• H10 Playing a high reservation value for teammembers (RUa = 0.65) will result in the high-est average team joint utility against Conceder,Boulware, and Nice Tit-for-Tat.

These types of teams (RUa = 0.35, RUa =0.5, RUa = 0.65) were faced in every scenario andnegotiation case against every type of opponent for20 repetitions. We gathered information on theteam joint utility and the utility obtained by theopponent, and an ANOVA (α = 0.05) with Bonfer-roni post-hoc analysis was carried out to determineresults that are statistically better than the rest.All of the claims of this experimental section aresupported by the ANOVA test with the Bonferronipost-hoc analysis.

Table 5 shows the results of this experiment interms of the average joint utility. A bold font styleis used to highlight those Bayesian team configura-tions that are statistically the best option againsteach opponent. Additionally, the same table showsthe proportion of negotiations that finished withsuccess (agreement) in this experiment. Table 4shows the average percentage of unpredictable par-tial offers that were pruned in the pre-negotiationdepending on the team configuration and team pref-erence similarity.

With respect to H10, it can be observed that in-dependently of the degree of dissimilarity amongteam members’ preferences, team members ob-tained statistically better team joint utility by set-ting high reservation utilities (RUa = 0.65) againstBoulware, Conceder, and Nice Tit-for-Tat oppo-nents. These results support our initial hypothesisH10.

Nevertheless, H9 is only partially supported.When facing Agent K, playing the highest reserva-tion utility configuration lead to the highest teamjoint utilities when team members’ preferences aresimilar or they have an average similarity (top andmiddle part of Table 5), which is opposite to ourinitial hypothesis H9. In this case, the demands ofthe team are still not high enough to preclude agree-ments with the competitor agent. However, whenteam members’ preferences are dissimilar (bottom

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SimilarAgent K Nice Tit-for-Tat Boulware Conceder

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.RUa = 0.35 0.195 100 0.117 100 0.160 100 0.526 100RUa = 0.50 0.263 100 0.164 100 0.224 100 0.557 100RUa = 0.65 0.350 99.98 0.286 100 0.354 100 0.635 100

Average SimilarityAgent K Nice Tit-for-Tat Boulware Conceder

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.RUa = 0.35 0.167 100 0.090 100 0.136 100 0.342 100RUa = 0.50 0.248 100 0.158 100 0.224 100 0.390 100RUa = 0.65 0.242 74.2 0.268 100 0.313 100 0.470 100

DissimilarAgent K Nice Tit-for-Tat Boulware Conceder

T. Joint % Ag. T. Joint % Ag. T. Joint % Ag. T. Joint % Ag.RUa = 0.35 0.193 100 0.115 100 0.173 100 0.373 100RUa = 0.50 0.209 86.6 0.196 100 0.271 100 0.475 100RUa = 0.65 0.068 18.3 0.346 100 0.409 100 0.580 100

Table 5: Average joint Utility (T. Joint) for teams composed by Bayesian team members with different reservation utilitiesand proportion of negotiations that finished with success (% Ag.).

part of Table 5), we can observe how setting a highreservation utility (i.e., RUa = 0.65) gradually be-comes the worst possible course of action when fac-ing Agent K, making H9 true for this situation. Thereason for this behavior is mainly explained due tothe decrease in the number of successful negotia-tions. If we observe the similar scenario, the num-ber of successful negotiations when facing Agent Kand RUa = 0.65 is 99.98%. If we change to aver-age similarity scenarios, the number of successfulnegotiations is 74.2% when facing Agent K withRUa = 0.65. The same measure is decreased to18.3% in the dissimilar scenario. If we observe Ta-ble 4, as team dissimilarity increases, the number ofunpredictable partial offers to be pruned is larger.This leaves less negotiation space to be played withAgent K. Agent K is a competitor agent that at-tempts to concede as less as possible by estimat-ing the maximum utility that can be obtained fromthe opponent and employing a limit of compromisewhen the opponent takes a hard stance. First of all,if reservation utilities are high, it can be consideredthat team members play a hard stance. Second,if too much negotiation space is pruned, it may befeasible that the set of remaining unpredictable par-tial offers precludes Agent K from reaching its limitof compromise. Thus, employing high reservationutilities against a competitor agent like Agent Kmay result, as we have observed in this case, in an

increase in the number of failed negotiations andlower team joint utilities.

In conclusion, H10 is supported by our findings,but H9 is only partially supported. We have ob-served that team members may benefit from playinghigh reservation utilities against Conceder, Boul-ware, and Nice Tit-for-Tat. If faced against com-petitors like Agent K, setting high reservation util-ities may prune too much negotiation space, espe-cially when team members are dissimilar. This re-sults in negotiation spaces that may not contain theminimum limits established by competitor agents,thus, ending negotiations with failure. For otherscenarios against agent K, the team can benefitfrom setting high reservation utilities since the re-sulting negotiation space still has room to accom-modate an agreement with the competitor agent.In general, team members should be cautious whensetting the reservation utility since it may end upin more failures.

6.5. Team performance with risk attitudes

One scenario that should be considered in multi-agent systems is agent’s attitude towards risk.Some team members may be more willing to chooseactions that guarantee a safer agreement, whileother may prefer to go for more profitable but lessprobable agreements. Classically, agents can showa risk seeking, a risk averse, and a risk neutral at-

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titude. The goal of this experiment is determin-ing how risk attitudes affect the performance of theproposed negotiation model. In this experiment, wedecided to test three different patterns of behavior:

• Risk averse team member: This team memberselects from the list of available unpredictablepartial offers (see Equation 7, those that guar-antee the current aspirations of the team mem-ber sa(t)) the best unpredictable partial of-fer according to the acceptance probability forthe opponent by using the Bayesian mecha-nism proposed in this article. When the teamsets predictable issue, the maximum utility ob-tainable with other unpredictable partial of-fers may be higher since they may provide ahigher utility of oneself. However, in order tosecure a deal, the team member selects the un-predictable partial offer that is supposed to bemore acceptable to the opponent even if themaximum achievable utility is lower. There-fore, the team member bases its choices on theacceptability of the offer by the opponent partyinstead of the maximum achievable utility.

• Risk seeking team member: This team memberselects for the list of available unpredictablepartial offers (see Equation 7) the best unpre-dictable partial offer according to the utilityreported by one’s own utility function. Hence,this unpredictable partial offer represents thechoice that enables the team member to getthe maximum achievable utility in the negoti-ation domain. By filling predictable issues bythe team, the team member is more likely toget closer to its maximum achievable utility,even if this action reduces acceptability of theproposed offer for the opponent.

• Risk neutral team member: This behavior isrepresented by the Bayesian team member pre-sented in this article.

Our initial hypothesis is that the proposed modelis robust to risk attitudes. By robustness, we meanthat the proposed negotiation model will be ableto obtain a team joint utility higher than or com-parable to the team joint utility obtained by otherstate-of-the-art models like SBV:

• H11 Different configurations of team mem-bers’ risk attitudes will yield a team joint util-ity that is statistically higher or equal to theresults obtained by SBV.

SimilarK N. TFT B. C.

Averse 0.241 0.160 0.238 0.372Neutral 0.259 0.164 0.224 0.557Mix 0.250 0.216 0.267 0.520Seeker 0.169 0.248 0.283 0.615SBV 0.181 0.150 0.184 0.552

Average SimilarityK N. TFT B. C.


DissimilarK N. TFT B. C.


Table 6: Team joint utility obtained by the different teamrisk configurations. K (Agent K), N. TFT (Nice Tit-for-Tat),B. (Boulware), C. (Conceder)

The experimental parameters of the previousexperiments were repeated (RUa = 0.5, βa =U [0.5, 1]), and we selected four different team con-figurations. The first one is composed by four neu-tral team members (Neutral), the second is com-posed by four risk seeking team members (Seeker),the third is composed by three risk averse teammembers (Averse), and the last team configura-tion is composed by two neutral team members,one risk seeker, and one risk averse (Mix). As inthe previous experiments, the team members faceddifferent opponent profiles in scenarios where teammembers’ preference profiles are similar, scenarioswith average similarity of team members’ prefer-ences, and scenarios where team members have dis-similar preferences. The team faces the same op-ponent strategies presented in the previous experi-ments. We gathered information on the team jointutility.

The results of this experiment can be found onTable 6. Results highlighted in bold represent thestatistically higher team joint utility configurationsfor each negotiation scenario (ANOVA, α = 0.05).As it can be observed, the risk seeking configura-tion usually gets a higher team joint utility as longas the opponent faced is not a competitor. Thisconfiguration is able to obtain one of the best team

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joint in all negotiation scenarios with Nice Tit-for-Tat, Boulware, and Conceder. When negotiatingagainst Agent K , many negotiations end with fail-ure since the opponent also has high aspirations.Other opponents like Nice Tit-for-Tat, Boulware,or Conceder match the high aspirations of the riskseeking team at one point or another of the negoti-ation, resulting in a higher team joint utility.

The mixed configuration usually gets the nexthighest team joint utility, being able to obtain sta-tistically equivalent results in some scenarios likenegotiating against Nice Tit-for-Tat in the averagesimilarity scenario, and statistically higher resultslike negotiations against Agent K in dissimilar sce-narios. This configuration obtains the best teamjoint utility in all of the scenarios involving againstAgent K.

The neutral configuration, obtains statisticallygood results in some scenarios where team membershave similar preferences and the Bayesian mecha-nism is able to learn the opponent preferences prop-erly (e.g., negotiating against Agent K, some sce-narios against Boulware and Nice Tit-for-Tat). Therisk averse configuration is only able to obtain someof the top results in very specific scenarios like ne-gotiations against in similar settings against AgentK.

However, in no case any of the team configura-tions proposed in this article is worse than SBV. Allof the results are statistically higher than those ob-tained by SBV, except for those obtained by the riskseeking configuration against Agent K, which arestatistically equivalent to those obtained by SBV.Therefore, despite being affected by team hetero-geneity, the proposed model is robust and it is ableto obtain results that are at least equal to the state-of-the-art (i.e., SBV), outperforming it in many sit-uations. This result supports our initial hypothesisH11.

7. Related Work

The contributions of this article to the auto-mated negotiation community can be divided intotwo different categories: general contributions tothe field of automated negotiation, and contribu-tions to the specific field of agent-based negotiationteams. Next, we analyze the contributions to eachof these fields.

7.1. Automated negotiation with single individualparties

The artificial intelligence community has focusedon bilateral or multi-party negotiations where par-ties are composed of single individuals. The maincontribution of our work with respect to the generalfield of automated negotiation is that we supportnegotiation parties composed by multiple individ-uals. Apart from that, in the next paragraphs wediscuss other contributions of our present negotia-tion framework with respect to works in automatednegotiation.

Faratin et al. (Faratin et al., 1998) introducedsome of the most widely used families of concessiontactics in negotiation. The authors proposed con-cession strategies for negotiation issues that are amix of different families of concession tactics. Theauthors divide these concession tactics into threedifferent families: (i) time-dependent concessiontactics; (ii) behavior-dependent concession tactics;and (iii) resource-dependent tactics. Our negotia-tion framework also considers time as crucial ele-ment in negotiation. Therefore, team members em-ploy time tactics inspired in those introduced byFaratin et al. However, the authors do not proposeany explicit preference learning mechanism.

In Zeng and Sycara (Zeng and Sycara, 1998), theauthors argue about the benefits of using Bayesianmodels in negotiation and they study a bilateralnegotiation case where the buyer attempts to learnthe reservation price of the seller by updating itsbeliefs with Bayesian learning. Despite the factthat it introduces the use of Bayesian learning innegotiation, the article only focuses on single issuemodels. One of our team member models also usesBayesian learning as a method for learning otheragents’ preferences. The main different resides inthe fact that our Bayesian approach attempts tomodel which instantiations of unpredictable issuesare acceptable for the opponent and the team inmulti-issue negotiations.

Ehtamo et al. (Ehtamo et al., 2001) proposea mediated multi-party negotiation protocol whichlooks for joint gains in an iterated way. The algo-rithm starts from a tentative agreement and movesin a direction according to what the agents preferregarding some offers’ comparison. Results showedthat the algorithm converges quickly to Paretooptimal points. However, the work proposed byEhtamo et al. does not support unpredictable is-sues and multiple individual parties.

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Klein et al. (Klein et al., 2003a) propose a me-diated negotiation model which can be extended tomultiple parties. Their main goal is to provide so-lutions for negotiation processes that use complexutility functions to model agents’ preferences. Thenegotiation attributes are binary and no longer in-dependent. Our work supports multiple individualparties and negotiation issues with unrestricted do-main (e.g., real, integer, discrete, binary, etc.).

In Coehoorn et al. (Coehoorn and Jennings,2004), the authors propose the use of kernel den-sity estimation for the estimation of the importanceweights of the linear additive utility function. Theagent calculates tuples composed of the differencebetween pairs of consecutive offers, the estimatedweight for the issue, and the probability densityof the weight. These tuples form a three dimen-sional kernel that is used along the other kernelsto calculate an estimation of the real issue weight.Our proposed model is capable of learning in nego-tiations where domains are also composed by dis-crete issues, which is not supported by Coehoornet al. Moreover, the learning mechanism proposedfor our team members deals with the information inone single negotiation, whereas the aforementionedmechanism learns over several negotiations.

Later, Narayanan et al.(Narayanan and Jennings,2006) present a negotiation framework where pairsof agents negotiate over a single issue. The authorsassume that agents’ strategies may change overtime. Non-stationary Markov chains and Bayesianlearning are employed to tackle the uncertainty inthis domain, and eventually converge towards theoptimal negotiation strategy. In our case, we fo-cus on one single negotiation process, and our teammembers learn over the information provided by thecurrent negotiation. Additionally, we consider ne-gotiations where multiple issues are involved.

Another example of the use of Bayesian learningin negotiation is presented by Buffett et al. (Buf-fett and Spencer, 2007). In the aforementioned ar-ticle, a bilateral framework is presented in a do-main where agents negotiate over a set of binaryissues. A Bayesian classifier is employed to classifyopponent’s preferences into classes of preference re-lations. Groups of similar preference relations aregrouped according to the k-means algorithm priorto the negotiation process. Our model does not re-quire learning prior to the negotiation, which mayrequire a costly learning process every negotiationto avoid domain dependent classifiers. Moreover,we consider any kind of issue type in the negotia-

tion domain.Carbonneau et al. (Carbonneau et al., 2008) pro-

pose a neural network that takes as input the nego-tiation history of a bilateral negotiation with con-tinuous issues and an offer to make an estimationof the opponent’s counter-offer. This approach re-quires that an artificial neural network is trainedper negotiation case. Similarly, the same authorspropose an improvement over their previous workin (Carbonneau et al., 2011). It aims to make apredictive model that does not depend on the ne-gotiation case. The model takes pairs of negotiationissues as inputs of the neural network, where one ofthe issues is considered the primary issue (i.e., inde-pendent variable) and the other issue is consideredthe secondary issue (i.e., dependent variable). Dif-ferently to these works, our proposed model doesnot rely on information from past negotiations. Itonly employs information gathered in the presentprocess.

Robu et al.(Robu and La Poutre, 2008) introducea bilateral negotiation model where agents repre-sent their preferences by means of utility graphs.The negotiation domain is formed of bundles ofitems that can be either included or excluded in afinal deal. Utility graphs are graphical models thatrelate negotiation issues that are dependent. Nodesrepresent negotiation issues whereas arcs connect is-sues that have some joint effect on the utility func-tion (i.e., positive for complementary issues, andnegative for substitutable issues). Hence, utilitygraphs represent binary dependencies between is-sues. The authors propose a negotiation scenariowhere the buyer’s preferences and the seller’s pref-erences are modeled through utility graphs. Theseller is the agent that carries out a more thor-ough exploration of the negotiation space in orderto search for agreements where both parties are sat-isfied. With this purpose, the seller builds a modelof the buyer’s preferences based on historic informa-tion of past deals and expert knowledge about thenegotiation domain. Our work does not considerdependencies between issues, however it is capableof supporting every type of domain for negotiationissues (i.e., real, binary, discrete, etc.).

In (Aydogan and Yolum, 2012), a concept-basedlearning method is proposed for modeling oppo-nent preferences and generating well-targeted of-fers. In that method, the preferences of the oppo-nent are represented via disjunctive and conjunc-tive constraints. In this article, our aim is also tofind the agreement earlier by means of learning the

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other participants’ preferences but the preferencesare represented by means of additive utility func-tions. In our case, an offer that is rejected by theopponent may become acceptable over time becausethe opponent may concede; therefore, we choose aprobabilistic learning method.

Williams et al. (Williams et al., 2012) presenta negotiation framework for coordinating multi-ple bilateral negotiations with different opponents.The agent simultaneously negotiates with differ-ent opponent in order to acquire a desired goodat the best possible condition. The frameworkmakes use of optimization techniques and proba-bilistic information in order to carry out this coor-dination. Similarly, Mansour et al. (Mansour andKowalczyk, 2012) present a meta-strategy for coor-dination multiple negotiations with different sellers.The meta-strategy adjusts the concession speed ac-cording to the current state of the multiple nego-tiation threads. The problem of agent-based nego-tiation teams is different since multiple agents col-laborate in the same party to get a deal from anopponent, instead of competing between each otherto get an individual deal.

7.2. Agent-based negotiation teams

As far as we are concerned, only our previ-ous works (Sanchez-Anguix et al., 2011, 2012a,b)have considered negotiation teams in computa-tional models. In (Sanchez-Anguix et al., 2011,2012a) four different computational models for anegotiation team negotiating with a single oppo-nent are presented. These four models attemptto gather four different minimum levels of una-nimity regarding team decisions: representative ap-proach (RE, no unanimity), similarity simple voting(SSV, majority/plurality), similarity Borda voting(SBV, semi-unanimity), and full unanimity medi-ated (FUM, unanimity).

The RE model is based on the selection of teammembers as representative of the team. The rep-resentative acts on behalf of the group by takingdecisions according to its own negotiation strategyand utility function.

SSV and SBV are models based on the presenceof a mediator that coordinates voting processes. Inthe case of SSV, a majority voting is employed todetermine whether or not the opponent’s offer isaccepted, and a majority voting is used to selectwhich offer is sent from those offers proposed byteam members to be sent to the opponent. In thecase of SBV, a unanimity voting is designated as

the mechanism to decide if opponent’s offers areaccepted and Borda count is used to decide whichoffer proposed by team members is sent to the oppo-nent. In both cases, SSV and SBV team membersdecide which offers are sent to the opponent usingsimilarity heuristics that consider the opponent’sand team’s last offers.

FUM is a mediated model where the opponent’soffers are evaluated by means of a unanimity vot-ing process, and team’s offers are built issue perissue by aggregation rules. These models were in-troduced at AAMAS 2011 (Sanchez-Anguix et al.,2011) as the first approach to tackle problems in-volving negotiation teams.

Later, we studied the special properties ofFUM, given that it was the intra-tem negotiationmodel capable of guaranteeing unanimity regardingteam decisions at each negotiation round (Sanchez-Anguix et al., 2012b). We proved how unanimityis guaranteed in FUM, how the intra-team strat-egy us robust against certain types of manipulationattacks, and how team members did not have incen-tive to strongly deviate from the proposed model.

We provided a full fledged experimental analysisof the four intra-team strategies in different negoti-ation environments (Sanchez-Anguix et al., 2012a).The results showed that FUM was able to guaranteebetter results for the negotiation team in most ne-gotiation scenarios. Only SBV is able to guaranteesimilar results in a limited number of negotiationcases.

Even though these four models cover differentlevels of unanimity with regards to team decisions,they were initially designed to provide solutions fornegotiation domains that are exclusively composedby predictable and compatible issues among teammembers (e.g., price, quality, and dispatch time ina team of buyers).

Domains exclusively composed by compatible andpredictable issues among team members cover arange of feasible negotiation domains. However, arelatively large number of negotiation domains alsoinclude unpredictable issues among team members.RE, SSV, and SBV can be easily adapted to do-mains that include unpredictable issues among teammembers by using a different similarity heuristic.FUM, the model that guarantees unanimity withregards to team decisions, cannot be used in thesedomains since, in the offer proposal mechanism, itaggregates issue values based on the fact that all ofthe negotiation issues are compatible and predictableamong team members.

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As stated, whenever it is possible, it is desirablefor the final agreement to be unanimously accept-able for all of the team members since the oppo-site situation may end up in users perceiving un-fairness, which may affect commitment to the deci-sion, group attachment, and trust (Korsgaard et al.,1995), and users that are not satisfied with agree-ments found automatically may end up leaving theelectronic application.

The model proposed in this article advances thestat of the art in agent-based negotiation teamsby solving both problems: it guarantees unanim-ity with regards to team decisions, and it sup-ports unpredictable negotiation issues, which werenot specifically supported in previous models. Forthat matter, the negotiation domains is split be-tween those issues that are compatible and pre-dictable among team members, and those issuesthat are unpredictable. In the former case, partof the mechanism employed in FUM is employed.By doing so, the model is capable of guarantee-ing that team members are able to get as much asthey need from predictable and compatible issues.In the latter case, the team discards those com-binations of unpredictable partial offers that pre-clude the team from reaching unanimously accept-able agreements, even if the most is obtained frompredictable and compatible issues. Then, in the offerproposal mechanism team members select one of re-maining unpredictable partial offers, and completethe predictable and compatible issue with the val-ues that they need to make it at least unanimouslyacceptable. The idea behind this splitting, is coop-erating as much as possible on those issues that arepredictable and compatible among team membersto create less intra-team conflict in unpredictableissues.

8. Conclusions & Future Work

In this article we have presented a new me-diated team negotiation model for a team as amulti-individual party negotiating with an oppo-nent in the alternating offers protocol. The presentmodel is capable of assuring unanimously accept-able agreements for all of the team members. Ittakes advantage of the categorization of negotia-tion issues as predictable and compatible, and un-predictable. The former are those issues whosepreferential order over issue values is known fromthe negotiation domain and it is common amongteam members (e.g., price in a team of buyers),

whereas the latter are those issues whose prefer-ential order over issues values is not known in thenegotiation domain. In the case of predictable andcompatible issues, there is full potential for coop-eration among team members since if one of theteam members demands more from the issue, theother team members are also benefited. Our negoti-ation model takes advantage of this property. Dur-ing the pre-negotiation, each team member shareswith a team mediator those unpredictable partialoffers (i.e., partial offers that have all of the unpre-dictable issues instantiated) that, even if the teamdemands the most from predictable issues, precludethe agent from achieving its reservation value. Ajoint list forbidden unpredictable partial offers isconstructed by the team mediator from the lists re-ceived from the team members. In the negotiation,the team mediator coordinates a unanimity votingprocess to decide whether or not to accept offersreceived from the opponent. As for the mechanismemployed to decide on which offer should be sent tothe opponent, the team mediator coordinates twoprocesses: a proposing and voting process whereeach team member suggests an unpredictable par-tial offer not included in the forbidden list followedby a Borda voting on candidates received, and aniterated process where predictable issues are set is-sue per issue attending to the demands of the teammembers.

We have proposed two different types of teammembers for the current model: a basic team mem-ber that proposes unpredictable partial offers dur-ing the negotiation solely guided by its own utilityfunction, and a Bayesian team member that sug-gests unpredictable partial offers based on the pref-erences of the team and the preferences of the op-ponent. Results have shown that, as long as pref-erential conflict is present in the team, team mem-bers have an incentive to employ the Bayesian strat-egy over the basic strategy. In any case, we haveshown that both approaches outperform other ex-isting models for negotiation teams. Moreover, wehave determined that when two negotiation teamsface each other, both teams benefit from includ-ing Bayesian team members in the negotiation. Fi-nally, we have shown that team members may ben-efit from playing higher reservation utilities againstconceders, matchers and inverters. Nevertheless,setting high reservation utilities may become theworst option as team members’ preferences aremore dissimilar and the opponent plays a competi-tor strategy.

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The topic of agent-based negotiation teams re-mains largely unexplored compared to negotiationinvolving single individual parties. The presentwork has focused on agent-based negotiation teamswhere team members have different preferences butthey share the same knowledge regarding the nego-tiation domain. One potential area of research ismodeling negotiation teams where team membersdiffer in their knowledge of the negotiation domainand their skills related to the negotiation process.As another line of future work, one could considerthe problem of forming negotiation teams based onthe individual list of unpredictable partial offers.Lists that are more similar may suggest team mem-bers that are more similar, which, if put togetherin the same team, may result in more cooperativeteams. Related to team formation, dynamic nego-tiation teams where team members may join andleave the team during the negotiation can be con-sidered an alternative line of research.

Acknowledgements

This research is partially supported by TIN2012-36586-C03-01 of the Spanish government andPROMETEOII/2013/019 of Generalitat Valen-ciana. Other part of this research is supportedby the Dutch Technology Foundation STW, ap-plied science division of NWO and the TechnologyProgram of the Ministry of Economic Affairs; thePocket Negotiator project with grant number VICI-project 08075.

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Unanimously Acceptable Agreements for Negotiation Teams in Unpredictable Domains

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