Automated Negotiation: Prospects, Methods and Challenges · Automated Negotiation: Prospects, Methods and Challenges N. R. Jennings1, P. Faratin2, ... either a single complete proposed

To appear in: Int Journal of Group Decision and Negotiation GDN2000 Keynote Paper

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Automated Negotiation: Prospects, Methods and Challenges

N. R. Jennings1, P. Faratin2, A. R. Lomuscio3, S. Parsons4, C. Sierra5 and M. Wooldridge4

1 Dept. of Electronics and Computer Science, University of Southampton,Southampton SO17 1BJ, [email protected]

2 Dept. of Electronic Engineering, Queen Mary and Westfield College,University of London, London E1 4NS, UK.

[email protected]

3 Dept. of Computing, Imperial College of Science, Technology and Medicine,London SW7 2BZ, UK.

[email protected]

4 Dept. of Computer Science, University of Liverpool,Liverpool L69 7ZF, UK.

{s.d.parsons, m.j.wooldridge}@csc.liv.ac.uk

5 Artificial Intelligence Research Institute, Spanish Scientific Research Council,Campus UAB, 08193 Bellaterra, Barcelona, Spain.

[email protected]


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1. Introduction

An increasingnumberof computersystemsarebeingviewedin termsof autonomousagents.

Therearetwo maindriversto thistrend.Firstly,agentsarebeingadvocatedasanextgeneration

modelfor engineeringcomplex,distributedsystems[13], [44]. Secondly,agentsarebeingused

asan overarchingframeworkfor bringing togetherthe componentAI subdisciplinesthat are

necessaryto designandbuild intelligent entities[24], [32]. While thereis still muchdebate

abouttheprecisenatureof agenthood,anincreasingnumberof researchersfind thefollowing

characterisation useful [44]:

an agent is an encapsulatedcomputersystemthat is situatedin someenvironment

and that is capableof flexible, autonomousaction in that environmentin order to

meet its design objectives

Thereare a numberof points about this definition that requireelaboration.Agentsare: (i)

clearly identifiableproblemsolving entitieswith well-definedboundariesand interfaces;(ii)

situated(embedded)in a particularenvironment—they receive inputs relatedto the stateof

their environment throughsensorsand they act on the environment througheffectors; (iii)

designedto fulfill a specificpurpose—they have particularobjectives(goals)to achieve; (iv)

autonomous—they havecontrolbothover their internalstateandover theirown behaviour; (v)

capableof exhibiting flexible problemsolvingbehaviour in pursuitof theirdesignobjectives—

they needto bebothreactive (ableto respondin a timely fashionto changesthatoccurin their

environment) and proactive (able to act in anticipation of future goals) [45].

Whenadoptinganagent-orientedview of computation,it is readilyapparentthatmostproblems

requireor involvemultipleagents: to representthedecentralisednatureof theproblem,themul-

tiple loci of control, the multiple perspectivesand/orthe competinginterests[6]. Moreover,

theseagentswill needto interactwith oneanother, eitherto achieve their individual objectives

or to managethedependenciesthat follow from beingsituatedin a commonenvironment[7],


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[14]. Theseinteractionscanvary from simpleinformationinterchanges,to requestsfor partic-

ularactionsto beperformedandon to cooperation(working togetherto achieveacommonob-

jective)andcoordination(arrangingfor relatedactivitiesto beperformedin acoherentmanner).

However,perhapsthemostfundamentalandpowerfulmechanismfor managinginter-agentde-

pendenciesat run-timeis negotiation—theprocessby which a groupof agentscometo a mu-

tually acceptableagreementon somematter.Negotiationunderpinsattemptsto cooperateand

coordinate(bothbetweenartificial andhumanagents)andis requiredbothwhentheagentsare

self interestedandwhentheyarecooperative.It is socentralpreciselybecausetheagentsare

autonomous.Foranagentto influenceanacquaintance,theacquaintanceneedsto beconvinced

that it shouldact in a particularway.Themeansof achievingthis stateareto makeproposals,

tradeoptions,offer concessions,and(hopefully)cometo a mutuallyacceptableagreement.In

short, to negotiate.

Givenits ubiquityandimportancein manydifferentcontexts,negotiationtheoryincorporatesa

broadrangeof phenomenaandmakesuseof manydifferentapproaches(e.g.from AI, Social

PsychologyandGameTheory).Despitethis variety,however,automatednegotiationresearch

canbe consideredto dealwith threebroadtopics(see[21] for a moredetailedclassification

scheme):

• NegotiationProtocols: thesetof rulesthatgoverntheinteraction.Thiscoverstheper-

missibletypesof participants(e.g.thenegotiatorsandany relevant third parties),the

negotiationstates(e.g.acceptingbids,negotiationclosed),theeventsthatcausenego-

tiation statesto change(e.g.no morebidders,bid accepted)andthe valid actionsof

the participantsin particularstates(e.g. which messagescan be sentby whom, to

whom, at what stage).


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• Negotiation Objects: the rangeof issuesover which agreementmustbe reached.At

oneextreme,theobjectmaycontaina singleissue(suchasprice),while on theother

hand it may cover hundredsof issues(relatedto price, quality, timings, penalties,

termsandconditions,etc.).Orthogonalto theagreementstructure,anddeterminedby

the negotiationprotocol,is the issueof the typesof operationthat canbeperformed

on agreements.In the simplestcase,the structureandthe contentsof the agreement

arefixedandparticipantscaneitheracceptor rejectit (i.e. a take it or leave it offer).

At thenext level, participantshave theflexibility to changethevaluesof theissuesin

thenegotiationobject(i.e. they canmake counter-proposalsto ensurethe agreement

better fits their negotiation objectives). Finally, participantsmight be allowed to

dynamically alter (by adding or removing issues)the structureof the negotiation

object(e.g.a carsalesmanmayoffer oneyear’s free insurancein orderto clinch the

deal).

• Agents’ Decision Making Models: the decisionmaking apparatusthe participants

employ to actin line with thenegotiationprotocolin orderto achieve theirobjectives.

The sophisticationof the model, as well as the rangeof decisionsthat have to be

made,areinfluencedby theprotocolin place,by thenatureof thenegotiationobject,

and by the range of operations that can be performed on it.

Therelativeimportanceof thesethreetopicsvariesaccordingto thenegotiationandenviron-

mentalcontext.Thus,in somecircumstancesthenegotiationprotocolis thedominantconcern

(e.g.[33], [43]). For example,thesystemdesignermaydeterminethat thenegotiationis best

organisedusinga particularform of auction(e.g.English,Dutch,Vickrey, First-PriceSealed

Bid). This mechanismdesignchoiceconstrainsthe typesof operationsthatcanbeperformed


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on thenegotiationobject(no counter-proposalsor issueextensions)andprescribesthebehav-

iour of theagents’decisionmakingmodels(e.g.strategicbehaviouris pointlessandtheagents’

dominantstrategyis to simply bid up to their truereservationvalue).In othercases,however,

theagent’sdecisionmakingmodelis thedominantconcern(e.g.[37], [40]). Here,theprotocol

doesnotprescribeanoptimalstrategyfor theagentandthereis scopefor strategicreasoningto

determinethebestcourseof action.In suchcases,therelativesuccessof two agentsis deter-

mined by the effectivenessof their reasoningmodel—thebetter the model, the greaterthe

agent’s reward.

Given the wide variety of possibilities,it shouldbe clearthat thereis no universallybestap-

proachor techniquefor automatednegotiation.Rather,thereis aneclecticbagof methodswith

propertiesandperformancecharacteristicsthatvarysignificantlydependingon thenegotiation

context.Theaim of this paperis, therefore,to examinethespaceof negotiationopportunities

for autonomousagents,to identify andevaluatesomeof the key techniques,andto highlight

someof themajorchallengesfor futureautomatednegotiationresearch.Thispaperis notmeant

asa surveyof the field of automatednegotiation.Rather,thedescriptionsandassessmentsof

thevariousapproachesaregenerallyundertakenwith particularreferenceto work in which the

authorshavebeeninvolved. However,the specific issuesraisedshouldbe viewed as being

broadly applicable.

Theremainderof thispaperis structuredasfollows.Section2 presentsagenericframeworkfor

automatednegotiation.This frameworkis thenusedto structurethesubsequentdiscussionand

analysisof thevariousnegotiationtechniques;section3 dealswith gametheoretictechniques,

section4 with heuristictechniques,andsection5 with argumentation-basedtechniques.Finally,

section6 outlinessomeof themajorchallengesthatneedto beaddressedbeforeautomatedne-

gotiation becomes pervasive.


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2. A Generic Framework for Automated Negotiation

Negotiationcanbeviewedasadistributedsearchthroughaspaceof potentialagreements(fig-

ure1). Thedimensionalityandtopologyof this spaceis determinedby thestructureof thene-

gotiationobject.Indeed,onecouldconsidereachattributeof thenegotiationobjectto havea

separatedimensionassociatedwith it; clearly,in this view, thespaceof figure 1 concernstwo

attributes.Thus,whennewissuesareadded(or old onesremoved)duringthecourseof anego-

tiation, thenextradimensionsareadded(or removed)andthenumberof pointsof agreement

may increase(or decrease).Similarly, if an agentchangesoneof the valuesof oneof the at-

tributes within an offer, it is moving from one point in the agreement space to another.

Foragivennegotiation,theparticipantsaretheactivecomponentsthatdeterminethedirection

of thesearch.At thestartof this process,eachagenthasa portionof thespacein which it is

willing to makeagreements.Typically, it alsohassomemeansof ratingthepointsin its space

andsomemeansof usingthis ratingto determinetheactualagreementsit makes.Negotiation

proceedsby theparticipantssuggestingspecificpoints(or regions)in theagreementspaceas

potentiallyacceptable.During the negotiationprocess,the participants’agreementspaces(as

well astheir ratingfunctions)maychange:theymayexpand,contract,or shift, for examplebe-

causetheir environmentchangesor becausethey are persuadedto changetheir views. The

searchterminateswhentherequirednumberof participantsfind amutuallyacceptablepoint in

the agreementspaceor when the protocoldictatesthat the searchshouldbe terminated(for

whatever reason) without making an agreement.

Given this metaphor,figure 1 canbe seento representagentA1 negotiatingwith two other

agents(A2 andA3). Theagreementstructureis thesamein bothcases.Thecurrentoffer in the

A1-A3 negotiation(theseinteractionsarethelightly colouredexchanges)is in theareaof over-


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lapbetweenthetwo agentsmeaningthatit couldrepresentapotentialagreementbetweenthem.

Howeverthecurrentoffer in theA1-A2 negotiation(theseinteractionsarethedarkly coloured

exchanges)will not leadto anagreementsinceit is outsidetheagreementspaceof A2 (indeed

in thiscase,A1 andA2 currentlyhavenon-intersectingareasof agreementmeaningthatnodeal

is possible). For more on this metaphor for viewing the agreement space see [15], [20], [22].

Fromthis representation,it canbeseenthattheminimalnegotiationcapabilitiesare:(i) to pro-

posesomepartof theagreementspaceasbeingacceptable;and(ii) to respondtosuchaproposal

indicatingwhetherit is acceptable.In otherwords,theminimumrequirementof a negotiating

agentis theability to makeandrespondto proposals.Hereweconsideraproposalto beasolu-

tion to thenegotiationproblem;eithera singlecompleteproposedsolution,a singlepartialso-

lution, or a group of completeor partial solutions.In termsof the agreementspace,these

differentkindsof proposalsbecomeasinglepoint,aregionof thespace,asetof points,or aset

of regionsof thespace(for exampleapartialsolutionwouldbeanyregionof thespacein which

thequalitywasabovesomelevelandthepricebelowacertainthreshold).Generallyspeaking,

proposalscanbemadeeitherindependentlyof otheragents’proposalsor basedonthenegotia-

tion history.

Arguablythesimplestkind of negotiationwecanimagineis aDutchauction[31]. Theauction-

eer(oneagentin thenegotiation)callsout prices(negotiationobjectswith a singleattribute).

Whenthereis no signalof acceptancefrom theotherpartiesin theauction(otheragentsin the

negotiation)theauctioneermakesanewoffer which it believeswill bemoreacceptable(by re-

ducingtheprice).Here,becauseof theconvention(protocol)underwhichtheauctionoperates,

a lack of responseis sufficientfeedbackfor theauctioneerto infer a lack of acceptance.How-

everin anythingmorecomplexthanthis ratherspecialcase,theminimal requirementfor the


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“other agents”is that theyareableto indicatedissatisfactionwith proposalsthat theyfind un-

acceptable.

If agentscanonlyacceptor rejectothers’proposals,thennegotiation(andespeciallynegotiation

overobjectsthataremulti-dimensional)canbevery time consumingandinefficient sincethe

proposerhasnomeansof ascertainingwhy theproposalis unacceptable,norwhethertheagents

arecloseto anagreement,nor in which dimension/directionof theagreementspaceit should

movenext.Hencetheproposeris essentiallypickingpointsin theagreementspacebasedonits

perceptionof whatotherspreferandhopingthatit will eventuallystumbleuponsomethingac-

ceptable.To improvetheefficiencyof thenegotiationprocess,therecipientneedsto beableto

providemoreusefulfeedbackon theproposalsit receives.This feedbackcantaketheform of

a critique (commentson which partsof theproposaltheagentlikes or dislikes1) or a counter-

proposal(analternativeproposalgeneratedin responseto aproposal).Fromsuchfeedback,the

proposershouldbein a positionto generatea proposalthat is morelikely to leadto anagree-

ment (if it chooses to do so).

Considertheconceptof a critique first. A critiqueprovidestwo formsof feedback:(i) it sug-

gestsconstraintsonparticularnegotiationissuesand(ii) it indicatesacceptance/rejectionof par-

ticular parts of the proposal(or indeedof the whole proposal).To illustrate thesepoints,

consider the following short dialogues that are examples of proposals followed by critiques:

A: I propose that you provide me with service X under the following

conditions.

B: I am happy with the price of X, but the delivery date is too late.

1. To avoid introducing an unnecessarilylarge numberof different types of statement,we considersimple

accept/reject statements to be special cases of critiques.


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A: I propose that I will provide you with service Y if you provide me with

service X.

B: I don’t want service Y.

In thefirst case,thecritiqueindicatesthoseaspectsof theproposalthatareacceptableandthose

thatneedto bemodifiedandit alsosuggestsaconstraintononeof theissues(deliverydateear-

lier thanthecurrentsuggestion).In thesecondcase,thecritiqueindicatesoutrightrejectionof

partof theproposal.Generallyspeaking,themoreinformationplacedin thecritique,theeasier

it is for the original agent to determine the boundaries of its opponent’s agreement space.

Counter-proposalsarethesecondfeedbackmechanism.A counter-proposalis simplyapropos-

al thatis morefavourableto thesender,madein responseto apreviousproposal.Thefollowing

are examples of proposals followed by counter-proposals:

A: I propose that you provide me with service X.

B: I propose that I provide you with service X if you provide me with

service Z.

A: I propose that I provide you with service Y if you provide me with

service X.

B: I propose that I provide you with service X if you provide me with

service Z.

In the first case,the counter-proposalextendsthe initial proposal,and in the secondcaseit

amendspartof theinitial proposal.Counter-proposalsdiffer from critiquesin thatthefeedback

is lessexplicit (therecipientof a counter-proposalhasto infer theconstraintsandpreferences

from thewaytheproposalis re-constituted),butgenerallymoredetailed(sincespecificregions

of the opponent’s agreement space are identified).

On their own, proposals,critiques,andcounter-proposalsarebald statementsof what agents

want.Thus,their scopeis confinedsolelyto thestructureof thenegotiationobject.While it is


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perfectlypossibleto basenegotiationson just theseobject-levelconstructs(indeedthis is pre-

ciselywhatmostcurrentnegotiationmodelsdo),doingsodiminishessomeof thepotentialof

negotiation technology. For example, it means that agents cannot:

• Justify their negotiation stance;

An agentmighthaveacompellingreasonfor adoptingaparticularnegotiationstance.

For example,acompany maynotbelegally entitledto sellaparticulartypeof product

to a particulartypeof consumeror a particularitem maybeout of stockandthenext

delivery might not beuntil the following month.In suchcases,theability to provide

the justification for its attitudetowardsa particularissuecanallow the opponentto

more fully appreciate an agent’s constraints and behaviour.

• Persuade one another to change their negotiation stance;

Agentssometimesneedto actively changetheir opponents’agreementspace,or its

ratingover thatspace,in orderfor a dealto bepossible.In suchcases,agentsseekto

constructargumentsthat they believe will make their opponentlook morefavourably

upontheir proposal.Thus,argumentsseekto identify opportunitiesfor suchchange

(e.g.a car salesmanthrows in a stereowith a car to increasethe valueof the good),

createnew opportunitiesfor change(e.g.a carsalesmanaddsa new dimensionto the

rating function by highlighting the car’s novel securityfeatures)or modify existing

assessmentcriteria(e.g.carsalesmangetsthebuyerto changeits evaluationfunction

by convincing him that security is more important than high speed).

In bothcases,negotiatorsareprovidingargumentsto supporttheir stance(henceargumenta-

tion-basednegotiation). Thus,in additionto generatingproposals,counter-proposalsandcri-


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tiques,thenegotiatoris seekingto maketheproposalmoreattractive(acceptable)by providing

additionalmeta-levelinformationin theformof argumentsfor its position.Thenatureandtypes

of theargumentscanvaryenormously(see[16] [19] [40] for moredetails).However,common

categoriesinclude:threats(failure to acceptthis proposalmeanssomethingnegativewill hap-

pentoyou),rewards(acceptanceof thisproposalmeanssomethingpositivewill happentoyou),

andappeals(you shouldpreferthis optionoverthatalternativefor somereason).Whateverits

preciseform, the role of thesupportingargumentis eitherto modify the recipient’sregionof

acceptabilityor its ratingfunctionoverthis region.In sodoing,argumentshavethepotentialto

increasethe likelihood and/orthe speedof agreementsbeingreached;for example,if agents

preferargumentsthataremorelikely to leadto anagreement(which requiressomemetricon

theagreementspace)it ispossibletoprovethatargumentationleadstoquickeragreement[42]2.

In theformercase,by persuadingagentsto acceptdealsthattheymaypreviouslyhaverejected.

In thelattercase,by convincingagentsto accepttheiropponent’spositiononagivenissue(and

to cease negotiating over it).

3. Game Theoretic Models

Gametheoryis a branchof economicsthatstudiesinteractionsbetweenself-interestedagents.

Like decisiontheory,with whichit sharesmanyconcepts,gametheoryhasits rootsin thework

of vonNeumannandMorgenstern[23]. As its namesuggests,thebasicconceptsof gametheory

arosefrom thestudyof gamessuchaschess.However,it rapidly becameclearthat the tech-

niquesandresultsof gametheorycanequallybeappliedto all interactionsthatoccurbetween

2. Of coursepoorlydesignedargumentationsystemsalsohave thepotentialto increasethelengthof thenegotia-

tion unnecessarily, for exampleif agentskeeprepeatingthesameargumentsad infinitum. However, poordesign

of theotheraspectsof thenegotiationmechanismcanhavesimilarly adverseeffectsandsopotentiallyoverly long

negotiations are not something specific to argumentation-based negotiation.


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self-interestedagents.Gametheoryis relevantto thestudyof automatednegotiationbecause

the participants in such negotiations can reasonably be assumed to be self interested.

Theclassicgametheoreticquestionaskedof anyparticularmulti-agentencounteris: whatis the

best—mostrational—thing anagentcando?In mostmulti-agentencounters,theoverall out-

comewill dependcritically on thechoicesmadeby all agentsin thescenario.This impliesthat

in orderfor anagentto makethechoicethatoptimisesits outcome,it mustreasonstrategically.

That is, it musttakeinto accountthedecisionsthatotheragentsmaymake,andmustassume

thattheywill actsoasto optimisetheir ownoutcome.In negotiation,this means,for example,

takinginto accounttheprivatevaluationsthatagentshaveof thenegotiationissues,theirprivate

deadlinesfor makingadeal,andsoon.Gametheorygivesusawayof formalisingandanalys-

ing such concerns.

Negotiationandbargainingwerestudiedin the gametheory literaturewell beforethe emer-

genceof multi-agentsystemsasa researchdiscipline,andevenbeforethe adventof the first

digital computer.However,computersciencebringstwo importantconsiderationsto thegame

theoretic study of negotiation and bargaining:

1. Gametheoreticstudiesof rationalchoicein multi-agentencounterstypically assume

thatagentsareallowedto selectthebeststrategy from thespaceof all possiblestrate-

gies,by consideringall possibleinteractions.It turnsout thatthesearchspaceof strat-

egies and interactionsthat needsto be consideredhas exponentialgrowth, which

meansthat the problemof finding an optimal strategy is in generalcomputationally

intractable.In computerscience,thestudyof suchproblemsis thedomainof compu-

tationalcomplexity theory[26]. Thereis a significantliteraturedevotedto thedevel-

opmentof efficient (polynomialtime) algorithmsfor apparentlyintractableproblems,


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and the applicationof suchtechniquesto the study of multi-agentencountersis a

fruitful ongoing area of work.

2. Theemergenceof theInternetandWorld-Wide Webhasprovidedanenormouscom-

mercialimperative to the furtherdevelopmentof computationalnegotiationandbar-

gaining techniques [25].

Givenaparticularnegotiationscenariothatwill involveautomatedagents,gametheoretictech-

niques can be applied to two key problems:

1. The designof an appropriateprotocol that will govern the interactionsbetweenthe

negotiation participants. Theprotocoldefinesthe“rulesof encounter”betweenagents

[33]. Formally, a protocolis a setof normsthatconstraintheproposalsthatthenego-

tiation participants are able to make. It is possible to design protocolsso thatany par-

ticular negotiation history has certaindesirableproperties—this is mechanismdesign,

and is discussed in more detail below.

2. Thedesignof a particularstrategy (theagents’decisionmakingmodels)that individ-

ualagentscanusewhile negotiating—anagentwill aim to usea strategy thatmaxim-

ises its own individual welfare. A key difficulty here is that, typically, the strategies

that work bestin theorytendto becomputationallyintractable,andarehenceunusa-

ble by agents in practice.

As notedabove,mechanismdesigninvolvesthedesignof protocolsfor governingmulti-agent

interactions,suchthattheseprotocolshavecertaindesirableproperties.Possiblepropertiesin-

clude, for example [35] p204:


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• Guaranteedsuccess: A protocol guaranteessuccessif it ensuresthat, eventually,

agreement is certain to be reached.

• Maximising social welfare: Intuitively, a protocol maximisessocial welfare if it

ensuresthat any outcomemaximisesthe sum of the utilities of negotiation partici-

pants. If the utility of an outcome for anagent was simply defined in terms of the

amount of money thatagentreceived in theoutcome,thena protocolthatmaximised

social welfare would maximise thetotal amount of money “paid out”.

• Pareto efficiency: A negotiationoutcomeis said to be Paretoefficient if thereis no

other outcome that will make at least one agent betteroff without makingat leastone

other agent worseoff. Intuitively, if anegotiationoutcomeis not Paretoefficient, then

there is another outcome that will make atleastoneagenthappierwhile keepingeve-

ryone else at leastas happy.

• Individual rationality: A protocol is said to be individually rational if following the

protocol— “playing by the rules”—is in thebestinterestsof negotiationparticipants.

Individually rationalprotocolsareessentialbecausewithout them,thereis no incen-

tive for agents to engage in negotiations.

• Stability: A protocolis stableif it providesall agentswith anincentive to behave in a

particular way. The best-known kind of stability is Nashequilibrium: two strategiess

ands' are said to be in Nash equilibrium if under theassumptionthat one agent is

usings , the other can do nobetter than uses' , and vice versa.

• Simplicity: A “simple” protocolis onethatmakestheappropriatestrategy for a nego-


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tiation participant “obvious”. Thatis, a protocolis simpleif usingit, a participantcan

easily (tractably) determine the optimal strategy.

• Distribution: A protocolshouldideally be designedto ensurethat thereis no single

point of failure (such as a single arbitrator),andideally, so asto minimisecommuni-

cation between agents.

Thefactthatevenquitesimplenegotiationprotocolscanbeprovento havesuchdesirableprop-

ertiesastheseaccountsin no smallpartfor thesuccessof gametheoretictechniquesfor nego-

tiation [17]. As anexample,considerthemonotonicconcessionprotocolwith Zeuthenstrategy

[33] pp40-49.Themonotonicconcessionprotocolfor two negotiationparticipantsis asfollows.

Negotiationproceedsin asequenceof rounds,whereateveryround,eachagentputsforwarda

proposal.If theproposals“overlap”, thenagreementhasbeenreached.If theproposalsdo not

overlap,thennegotiationproceedsto afurtherround,wheretheagentseithermakea concession

orelseputforwardtheproposaltheymadeontheprecedinground.If neitheragentmakesacon-

cession,thennegotiationterminateswith a“conflict deal”.Thissimpleprotocolensuresthatne-

gotiation either monotonicallyproceedstowardsa solution, or else terminates.Now, what

strategyshouldanagentusewhenfacedwith suchaprotocol?Onepossibilityis to usetheZeu-

then strategy. This strategy essentially says that:

• the agentthat shouldconcedeis the onewith the mostto lose from the negotiation

breaking down;

• theconcessionthatshouldbemadeis theminimumrequiredto changethebalanceof

risk—so that the other agent is required to concede on subsequent rounds.


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Bothof thesepropertiescanbeformalisedquiteeasily[33] p43.It canbeprovedthatusingthe

Zeuthenstrategywhenplayingthemonotonicconcessionprotocolmeansagentswill cometo

reachagreementon a dealthat is Paretooptimal.Unfortunately,theZeuthenstrategyis not in

equilibrium; thereis an incentiveto deviatefrom thestrategyat the lastnegotiationstep[33]

p48.Moreover,the strategyis computationallycomplex,requiringan exponentialnumberof

calculationsof theagent’sutility functionateachnegotiationroundin orderto computetheop-

timal deal.Nevertheless,it is striking thatsuchasimpleandintuitive protocolcanbeprovento

have desirable properties.

Despitethesevery obviousadvantages,however,therearea numberof problemsassociated

with the use of game theory when applied to automated negotiation:

• Gametheoryassumesthat it is possibleto characterisean agent’s preferenceswith

respect to possible outcomes.Humans, however, find it extremelyhardto consistently

define their preferences over outcomes. In general, humanpreferences cannot be

characterised even by a simple orderingover outcomes,let aloneby numericutilities

[32] p475-480. In scenarios wherepreferencesareobvious(suchasthecaseof a per-

son buying aparticularCD andattemptingto minimisecosts),gametheoretictech-

niques may work well. With more complex (multi-issue) preferences, it is much

harder to use them.

• Thetheoryhasfailed to generatea general modelgoverningrationalchoicein inter-

dependentsituations[46]. Instead,the discipline hasproduceda numberof highly

specialisedmodelsthat are applicableto specific typesof interdependentdecision

making(e.g.thevon Neumann-Morgensternsolutionto two-persongames[23]). As

Binmore notes, in non-cooperative (a sub-branch of game theory) theories:


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...conclusions(of non-cooperative models) only apply to one specific

game. If the details of the rules are changedslightly, the conclusions

reached need no longer be valid [5] p. 196.

• Gametheorymodelsoftenassumeperfectcomputationalrationalitymeaningthatno

computationis requiredto find mutuallyacceptablesolutionswithin a feasiblerange

of outcomes.Furthermore,this spaceof possibledealsis often assumedto be fully

known by theagents,asis thepotentialoutcomevalues.Thisassumptionis rarelytrue

in mostrealworld cases;agentstypically know their own informationspace,but they

do not know thatof their opponent.However, evenif thejoint spaceis known, know-

ing thata solutionexistsis entirelydifferentto knowing whatthesolutionactuallyis.

Chessis aclassicexampleof thispoint.Thegamehasasolution—astrategy for white

or blackwhich is eithera win or a draw, but thesearchis computationallycomplex.

Therefore,the notion of perfectrationality, althoughuseful in designing,predicting

andproving propertiesof a system,is not altogetherusefulin practice.Firstly, it can-

not actuallybe attained:physical mechanismstake time to processinformationand

selectactions,hencethebehaviour of realagentscannotimmediatelyreflectchanges

in theenvironmentandwill generallybesub-optimal[39]. Secondly, it doesnot pro-

vide a meansof analysingthe internal designof an agent;one rational agentis as

good as another.

Despitetheseproblems,gametheoryis extremelycompellingasa tool for automatednegotia-

tion. In caseswhereit is possibleto characterisethepreferencesandpossiblestrategiesof ne-

gotiation participants, then game theory has much to offer.


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3. Heuristic Approaches

Themajormeansof overcomingtheaforementionedlimitationsof gametheoreticmodelsis to

useheuristicmethods.Suchmethodsacknowledgethatthereis a costassociatewith computa-

tion anddecisionmakingandsoseekto searchthenegotiationspacein anon-exhaustivefash-

ion. This has the effect that heuristic methodsaim to producegood, rather than optimal

solutions.Themethodsthemselvesmayeitherbecomputationalapproximationsof gametheo-

retictechniquesor theymaybecomputationalrealisationsof moreinformalnegotiationmodels

(e.g.[29], [30]). Examplesof suchmodelsinclude:[3], [8], [18], [36], [41]. Thekeyadvantages

of the heuristic approach can be stated as follows:

• the modelsare basedon realistic assumptions;hencethey provide a more suitable

basisfor automationandthey can,therefore,beusedin a wider varietyof application

domains;

• thedesignersof agents,who arenot weddedto gametheory, canusealternative, and

less constrained, models of rationality to developdifferent agent architectures.

Thecentralconcernof this line of work is to modeltheagent’sdecisionmakingheuristically

duringthecourseof thenegotiation(generallyspeaking,thechosenprotocoldoesnotprescribe

anoptimalcourseof action).To delvedeeperinto thisareawewill concentrateontheheuristic

modelwehavedevised;wedevelopedasetof deliberationmechanismsthatwork within afair-

ly free negotiation protocol3 [8][9][10] [37].

The spaceof possibleagreementsis quantitativelyrepresentedby contractshavingdifferent

valuesfor eachissue.Eachagentthenratesthesepointsin thespaceof possibleoutcomesac-

cordingto somepreferencestructure,capturedby autility function.Proposalsandcounter-pro-


19

posalsare then offers over single points in this spaceof possibleoutcomes,and search

terminateseitherwhenthetime to reachanagreementhasbeenexceededor whena mutually

acceptablesolution,a point of intersectionof the agents’acceptableoutcomessets,hasbeen

reached.

An agentarchitecturethatmodelsthedecisionsinvolvedin thesearchfor mutuallyacceptable

solutionshasalsobeendeveloped[9]. Whereastheprotocolnormativelydescribestheorder-

ingsof actions,thedecisionmakingmechanismsdescribethepossiblesetof agentstrategiesin

usingtheprotocol.Thesestrategiesarecapturedby anegotiationarchitecturethatis composed

of responsiveanddeliberativedecisionmechanisms.Decisionmakingwith theformermecha-

nismis basedon a linearcombinationof simplefunctionscalledtactics, which manipulatethe

utility of contracts[8]. Thelattermechanismsaresubdividedinto trade-offandissuemanipu-

lation mechanisms[9]. The formergeneratesoffers thatmanipulatethevalue,ratherthanthe

overallutility, of theoffer.Therationalefor thetrade-offmechanism,like persuasiveargumen-

tation, is to makeproposalsthat aremoreattractiveto the opponent.This is achievednot by

“providing additionalmeta-levelinformation” (seesection4), but by providingcontractsthat

are“closer” to theopponent’slastoffer. The issuemanipulationmechanismaimsto increase

thelikelihoodof anagreementby addingandremovingissuesinto thenegotiationset.Theissue

3. The negotiation protocol doesnot prescribean agent’s behaviour, but it doesconstrainits action selection

problemsolvingthroughtheuseof normative rulesof interaction.Theserulestemporallyorder, accordingto the

agent’s roles,communicationutterancesby specifyingbothwho cansaywhat,aswell aswhen.Specifically, the

protocol is a repeated,sequentialmodelwhereoffers areiteratively exchanged.Underthis protocol,agentsare

fully committedto theirutterancesandutterancesareprivate(unlike,say, thefirst-priceopen-cryEnglishauction,

whereall offersarepublicly “heard”by theotherinteractionparticipants).Theprotocolis distributed,symmetric,

supportsbi and/ormulti-agentnegotiation as well as distributive and integrative negotiation, involving one or

many issuesrespectively. Theutterances(proposalsor counter-proposals)arebasedon previouscommentsmade

by otheragents,andrepresenta singlecompleteproposalfor a solution.Thereareno critiquesandcounter-pro-

posals are based on the object of negotiation (which we term a contract).


20

manipulationmechanismdynamicallyaltersthestructureof thenegotiationobject,helpingto

escapelocalminimain thenegotiationdynamics.It doesthiseitherby increasingthesetof pos-

sibleoutcomes(adding),whennegotiationis in deadlock,or, alternatively,removing“noisy”

issuesthatareobstructingthenegotiationprogress.Sinceagentshaveto mutuallyagreeon the

setof issuesinvolved in negotiation,the issuemanipulationdialoguecanbe interpretedasa

mechanismthatmodifiesthedimensionalityof thesolutionspace.Theothermechanisms,re-

sponsiveandtrade-off,canthensearchthealteredsolutionspace.Whentakentogether,these

threemechanismsrepresentacontinuumof possibledecisionmakingcapabilities:rangingfrom

behavioursthatexhibitgreaterawarenessof environmentalresourcesandlessto solutionqual-

ity, to behavioursthatattemptto acquireagivensolutionquality independentlyof theresource

consumption.

Generallyspeaking,while heuristicmethodsdo indeedcircumventsomeof theshortcomings

of game theoretic models, they also have a number of comparative disadvantages:

• the modelsoften selectoutcomes(deals)that are sub-optimal;this is becausethey

adoptan approximatenotion of rationality andbecausethey do not examinethe full

space of possible outcomes;

• the modelsneedextensive evaluation, typically throughsimulationsand empirical

analysis,sinceit is usually impossibleto predict preciselyhow the systemand the

constituent agents will behave in a wide variety of circumstances.

4. Argumentation-Based Approaches

All of the techniqueswe havediscussedsofar havebeencentredon the tradingof proposals.

Although,astheprevioussectionsdemonstrate,this canbedonein a very sophisticatedway,


21

the various approaches have three main limitations:

• The proposalsthemselvesgenerallydenotesinglepoints in the spaceof negotiation

agreements (a single X or O in Figure 1)4;

• Theonly feedbackthatcanbemadeto aproposalis acounter-proposal,which itself is

another point in the space, or an acceptance or withdrawal;

• It is hardto changethesetof issuesundernegotiationin thecourseof a negotiation

(which correspondsto changingthe negotiation spaceof Figure 1 by addingnew

dimensions).

Theaim of argumentation-basednegotiationis to removetheselimitations.Thebasicideabe-

hindtheargumentation-basedapproachis toallowadditionalinformationtobeexchanged,over

andaboveproposals.This informationcanbeof a numberof different forms,all of which are

argumentswhichexplainexplicitly theopinionof theagentmakingtheargument.Thus,in ad-

dition to rejectingaproposal,anagentcanoffer acritiqueof theproposal,explainingwhy it is

unacceptable.This hastheeffectof identifyinganentireareaof thenegotiationspaceasbeing

not worth exploringby theotheragent.Similarly, anagentcanaccompanya proposalwith an

argumentwhich sayswhy theotheragentshouldacceptit. This latterkind of argumentmakes

it possibleto changetheotheragent’sregionof acceptability(by alteringits preferences),and

alsoprovidesameansof changingthenegotiationspaceitself—without theability to arguefor

theworthof anewelementin thenegotiationobject,thereceivingagentwouldnot, in general,

haveanybasisonwhichto determineits value.Thiskind of persuasiveargumentationdoesnot

4. Though,of course,agentsreceiving proposalsmay assumeall kinds of implicit informationon the basisof

them.


22

haveto betieddirectly to proposalseither.Forexample,in humanargumentation,it is possible

to makethreatsor offer rewards,andthesekindsof argumentcanbecapturedin this approach

[19]. As in humanargumentation,agentsmaynot betruthful in theargumentsthattheygener-

ate.Thuswhenevaluatinganargument,therecipientneedsto assesstheargumenton its own

meritsandthenmodify thisby its ownperceptionof theargument’sdegreeof credibility in or-

der to work out how to respond.

Again to providemoredetailsof this broadclassof negotiation,we focuson modelswe have

developed.To thisend,thewayin whichargumentationfits into thegeneralnegotiationprocess

wasdefinedin [38] wherea simplenegotiationprotocolfor tradingproposalswasaugmented

with a seriesof illocutionarymoveswhich allow for thepassingof arguments.It is possibleto

think of thepassingof anargumentusingoneof thesemovesasmarkinga transitionfrom the

negotiationprotocolto a separateargumentationprotocolwhich definestherulesof thegame

for carryingoutanargumentdialogue(possibleprotocolsfor suchdialogueshavebeensuggest-

edin [1], [2]). Whentheargumentdialogueterminates,theagentsmakethereversetransition

and pick up the negotiation dialogue once again.

Theexactargumentationmechanismwe employis logic-based[27] andbuildson work in ar-

gumentationasanapproachto handlingdefeasiblereasoning.Thismakesit possiblefor agents

to handlingcontradictorystatements(which frequentlyoccurduring arguments)without col-

lapsinginto triviality, andallow conflicting argumentsto beresolved.Usingargumentationin

real agents(asopposedto simplecollectionsof logical statements)meanshandlingthe com-

plexitiesof theagents’mentalattitudes,communicationbetweenagents,andtheintegrationof

the argumentation mechanisms into a complex agent architecture.


23

Theseissueswerediscussedin [28], whereweshowedhowto augmentastandardmodelof ar-

gumentationto work for agentswhichreasonusingbeliefs,desiresandintentions.Wealsodis-

cussedhow to makeuseof multi-contextsystems[12], originally proposedas a meansof

providingefficient theoremproversfor modallogics,to integrateargumentationinto a belief-

desire-intentionagentarchitecture.Thislatterstrandof work wasfurtherdevelopedin [34], and

thishasledto animplementationin whichagentsnegotiateusingargumentationin orderto con-

struct joint plans.

Forthefuture,two mainareasof work remain.Thefirst is in thedefinitionof suitableargumen-

tationprotocols,thatis, setsof rulesthatspecifyhowagentsgenerateandrespondto arguments

baseduponwhattheyknow.Initial attemptsatdefiningsuchprotocolsaregivenin [1], [2], but

asdiscussedthere,it seemsthatwhendefininganargumentationprotocol,we “hard-wire” in

theattitudethata givenagenttakeswhennegotiatingwith others,defining,for instance,when

anargumentis foundto bepersuasive,andwhenits groundscanbequestioned.As aresult,we

mayendup with negotiatorswhich arepossiblyratherinflexible in their argumentationstance

(thoughmoreflexible thannegotiatorswhich cannotargue).Sincethis seemsratherlimiting,

we needto investigatethis areamorewith theaim of discoveringmoreflexible argumentation

protocolsthanwecurrentlyhave.Thesecondmainareaof work is alsorelatedto argumentation

protocols,andspecificallythe transitionbetweenthe underlyingnegotiationprotocolandthe

argumentationprotocol.Whenis theright time to makethis transition,whenis it right to start

anargument?Clearlyit only makessenseto engagein thecomplexbusinessof argumentation

whenit will helpthenegotiation,but we needto translatethis high-levelnotionof “rightness”

into some more concrete decision criterion that can be built into our agents.

While theseissuesstill needto beaddressedin orderto build fully functionalagentscapableof


24

argumentation-basednegotiation,thework describedin thissectionhaslaid thefoundationsfor

building flexible negotiators.Suchagentswill havetheability to bepersuasiveandsoachieve

agreementswhich non-argumentationbasednegotiatorscannot.However,the problemwith

suchmethodsis thattheyaddconsiderableoverheadsto thenegotiationprocess,not leastin the

constructionandevaluationof arguments.As a result,we imaginethatagentswhichcanargue

in supportof their negotiationswill only everrepresenta small,thoughimportant,classof au-

tomated negotiators.

5. Conclusions

This paperhasarguedthatautomatednegotiationis a centralconcernfor multi-agentsystems

research.To thisend,agenericframeworkfor classifyingandviewingautomatednegotiations

hasbeendeveloped.Thisframeworkwasthenusedto discussandanalysethethreemainmeth-

odsof approachthathavebeenadoptedto automatednegotiation;namely,gametheoretic,heu-

ristic andargumentation-basedapproaches.For eachapproach,a brief appraisalof its relative

meritsanddrawbacksis presented.This assessmentwasgenerallyperformedin thecontextof

the authors’ own models.

It is clearthatmuchresearchstill needsto beperformedin theareaof automatednegotiation.

This researchobviouslyincludesextendinganddevelopingthespecificapproachesthathave

beendiscussedhereinandevendevelopingnewmethods(suchasthosebasedon particledy-

namics[17], for example).However,therearealsoanumberof broaderissues,which, to date,

havereceivedcomparativelylittle attention.Theseincludethefollowing. Firstly, thedevelop-

mentof a bestpracticerepositoryfor negotiationtechniques.That is, a coherentresourcethat

describeswhich negotiationtechniquesarebestsuitedto a given type of problemor domain

(muchlike theway thatdesignpatternsfunction in object-orientedanalysisanddesign[11]).


25

Foreachentry,therelativestrengthsandweaknessesneedto beenumerated,theunderpinning

assumptionsneedto be explicitly stated,andthe likely operationalcharacteristicsneedto be

listed.At present,muchof this knowledgeis implicit anddeveloperstendto simply adoptthe

technique(or family of techniques)with which they are most familiar. Secondly,work on

knowledgeelicitation and acquisitionfor negotiationbehaviourneedsto be advanced.At

present,thereis virtually no work on how a usercaninstructanagentto negotiateon their be-

half.Suchinstructionneedsto conveythebroadnegotiationattitudethattheagentshouldadopt,

theextentto which theagentcannegotiateautonomously,andthedegreesof freedomthatthe

agentcanexploreduringanegotiationepisode.Finally, andrelatedto theprevioustwo points,

work onproducingpredictablenegotiationbehaviourneedsto bedeveloped.Thiswork is need-

edto ensurethatusersarecomfortableto delegatenegotiationdecisionsto anautonomouspiece

of softwareandthatwhentheydo sotheyaresurethattheagentwill actwithin its negotiation

mandate.

Acknowledgements

This work hasbeenpartially supportedby theEPSRCunderthegrantGR/M07076andby the

EU under grant IST-1999-10948.

References

[1] L. Amgoud,N. Maudet,andS. Parsons(2000)“Modelling dialoguesusingargumenta-

tion” Proceedings of the 4th Conference on Multi-Agent Systems, Boston, MA, 31-38.

[2] L. Amgoud,S. Parsons,andN. Maudet(2000)“Arguments,dialogue,andnegotiation”

Proceedingsof the14thEuropeanConferenceon Artificial Intelligence, Berlin, Germa-

ny, 338-342.


26

[3] M. BarbuceanuandW. Lo (2000)“A multi-attributeutility theoreticnegotiationarchitec-

turefor electroniccommerce”Proceedingsof 4th Int. Conf.onAutonomousAgents, Bar-

celona, Spain, 239-247.

[4] K. Binmore (1990) “Essays on the foundations of game theory” Basil Blackwell.

[5] K. Binmore (1992) “Fun and Games: A Text on Game Theory” D. C. Heath and Co.

[6] A. H. BondandL. Gasser(eds.)(1988)“Readingsin DistributedArtificial Intelligence”

Morgan Kaufmann.

[7] C.Castelfranchi(1998)“Modelling socialactionfor AI agents”Artificial Intelligence103

(1-2) 157-182.

[8] P.Faratin,C. Sierra,andN. R. Jennings(1998)“NegotiationDecisionFunctionsfor Au-

tonomous Agents”Int. Journal of Robotics and Autonomous Systems24 (3-4) 159-182.

[9] P.Faratin,C.Sierra,N. R.JenningsandP.Buckle(1999)“DesigningResponsiveandDe-

liberativeAutomatedNegotiators”Proc. AAAI Workshopon Negotiation:SettlingCon-

flicts and Identifying Opportunities, Orlando, FL, 12-18.

[10] P.Faratin,C. SierraandN. R. Jennings(2000)“Using Similarity Criteriato MakeNego-

tiation Trade-Offs”Proc. 4th Int. Conf on Multi-Agent Systems, Boston, USA, 119-126.

[11] E. Gamma,R. Helm, R. JohnsonandJ. Vlissides(1995)“DesignPatterns:Elementsof

Reusable Objected-Oriented Software” Addison Wesley.

[12] F.GiunchigliaandL. Serafini(1994)“Multilanguagehierarchicallogics(or: How wecan

do without modal logics)”Artificial Intelligence 65 29-70.

[13] N. R. Jennings(2000) “On Agent-BasedSoftwareEngineering”Artificial Intelligence

117 (2) 277-296.

[14] N. R. Jennings(1993)“CommitmentsandConventions:TheFoundationof Coordination

in Multi-Agent Systems”The Knowledge Engineering Review 8 (3) 223-250.


27

[15] N. R. Jennings,S. Parsons,C. Sierraand P. Faratin(2000) “AutomatedNegotiation”

Proc. 5th Int Conf.on Practical Applicationof IntelligentAgentsandMulti-AgentSys-

tems (PAAM-2000), Manchester, UK, 23-30.

[16] M. Karlins and H. I. Abelson (1970) “Persuasion” Crosby Lockwood and Son.

[17] S. Kraus(1997)“NegotiationandCooperationin Multi-Agent Environments”Artificial

Intelligence 94 79-97.

[18] S. Kraus and D. Lehmann(1995) “Designing and building an automatednegotiation

agent”Computational Intelligence 11 (1) 132-171

[19] S.Kraus,K. SycaraandA. Evenchik(1998)“Reachingagreementsthroughargumenta-

tion: a logical model and implementation”Artificial Intelligence 104 1-69.

[20] B. Laasri,H. Laasri,S. LanderandV. Lesser(1992)“A genericmodelfor negotiating

agents”Int. Journal of Intelligent and Cooperative Information Systems, 1(2), 291-317.

[21] A. R. Lomuscio,M. WooldridgeandN. R. Jennings(2000)“A classificationschemefor

negotiationin electroniccommerce”in Agent-MediatedElectronicCommerce:A Euro-

pean Perspective(eds. F. Dignum and C. Sierra), Springer Verlag, 19-33.

[22] R.Loui andD. Moore(2000)“DialogueandDeliberation”CognitiveScience(submitted).

[23] J. Von NeumannandO. Morgenstern(1944)“TheTheoryof GamesandEconomicBe-

haviour” Princeton University Press.

[24] N. J. Nilsson (1998)“Artificial Intelligence: A New Synthesis” Morgan Kaufmann.

[25] P. NoriegaandC. Sierra(eds.)(1999) “AgentMediatedElectronicCommerce” LNAI

Volume 1571, Springer-Verlag.

[26] C. H. Papadimitriou (1994) “Computational Complexity” Addison-Wesley.

[27] S.ParsonsandN. R. Jennings(1996)“NegotiationThroughArgumentation—APrelim-

inary Report”Proc. 2nd Int. Conf. on Multi-Agent Systems, Kyoto, Japan, 267-274.


28

[28] S.Parsons,C. SierraandN. R. Jennings(1998)“Agentsthatreasonandnegotiateby ar-

guing” Journal of Logic and Computation8 (3) 261-292.

[29] D. G. Pruitt (1981) “Negotiation Behaviour” Academic Press.

[30] H. Raiffa (1982) “The Art and Science of Negotiation” Harvard University Press.

[31] J.A. Rodriguez-Aguilar,F. J.Martin, P.Noriega,P.Garcia,C. Sierra(1998)“Towardsa

tesbed for trading agents in electronic auction markets”AI Communications 11 5-19.

[32] S. RussellandP. Norvig (1995) “Artificial intelligence:a modernapproach” Prentice

Hall.

[33] J. S. Rosenschein and G. Zlotkin (1994) “Rules of Encounter” MIT Press.

[34] J.Sabater,C. Sierra,S.ParsonsandN. R. Jennings(1999)“Using multi-contextsystems

to engineerexecutableagents”Proc.6th Int. Workshopon AgentTheoriesArchitectures

and Languages, Orlando, FL. 131-148.

[35] T. W. Sandholm(1999)“DistributedRationalDecisionMaking” in MultiagentSystems

(ed. G. Weiss) MIT Press, 201-258.

[36] A. SathiandM. S.Fox(1989)“Constraintdirectednegotiationof resourceallocation”in

L. GasserandM. Huhns(eds.)DistributedArtificial IntelligenceII , 163-195,Morgan

Kaufmann.

[37] C. Sierra,P. FaratinandN. R. Jennings(1997)“A Service-OrientedNegotiationModel

betweenAutonomousAgents”Proc.8thEuropeanWorkshoponModellingAutonomous

Agents in a Multi-Agent World, Ronneby, Sweden, 17-35.

[38] C.Sierra,N. R.Jennings,P.Noriega,andS.Parsons(1997)“A Frameworkfor Argumen-

tation-BasedNegotiation”Proc.4th Int. WorkshoponAgentTheories,Architecturesand

Languages,Rode Island, USA 177-192.

[39] H. A. Simon (1982) “Models of Bounded Rationality, Volume 2” MIT Press.


29

[40] K. Sycara(1989)“Argumentation:PlanningotherAgents’ Plans”Proc 11th Int. Joint.

Conf on AI, Detroit, MI., 517-523.

[41] K. Sycara(1989)“Multi-agent compromisevia negotiation”in L. GasserandM. Huhns

(eds.)Distributed Artificial Intelligence II, 119-139, Morgan Kaufmann.

[42] F. Tohme(1997) “Negotiation and defeasiblereasonsfor choice”, Proc AAAI Spring

Symposium on Qualitative preferences in deliberation and practical reasoning, 95-102.

[43] N. Vulkan andN. R. Jennings(2000)“Efficient Mechanismsfor theSupplyof Services

in Multi-Agent Environments”Int Journal of Decision Support Systems, 28 (1-2) 5-19.

[44] M. Wooldridge(1997)“Agent-basedsoftwareengineering”IEEProcSoftwareEngineer-

ing 144 (1) 26-37.

[45] M. WooldridgeandN. R. Jennings(1995)“Intelligent agents:theoryandpractice”The

Knowledge Engineering Review 10(2) 115-152.

[46] D. ZengandK. Sycara(1997)“How cananagentlearnto negotiate?”in J. Müller, M.

Wooldridge and N. R. Jennings,Intelligent Agents III, 233-244, Springer Verlag.


30

A1A2

X

X XXX

X

XXX

XX

XX

XX

XA3

Ai’s current region of acceptability

Ai’s initial region of acceptability

Figure 1: The Space of Negotiation Agreements

Previous offer

Current Offer

X

O

O

Ai

Ai

O

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