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Problem Restructuring in Negotiation

Author(s): Katia P. SycaraSource: Management Science, Vol. 37, No. 10, Focussed Issue on Group Decision and Negotiation(Oct., 1991), pp. 1248-1268Published by: INFORMSStable URL: http://www.jstor.org/stable/2632399

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MANAGEMENT SCIENCEVol. 37, No. 10, October 1991

Printed itn U.S.A.

PROBLEM RESTRUCTURING IN NEGOTIATION*K ATIA P. SYCARA

School of Compuptercience, CarnegieMellon University, Pittsbursgh,Pennsy)lvania15213To achieve movement towardsa negotiated settlement, it is often necessary to restructure heproblem under negotiation. Problem restructuringcan lead to changed perception of the issues

by the parties, thus breaking deadlocks and increasing the parties' willingness to compromise.We present a frameworkand mechanisms for problem restructuringbased on the goals and goalrelationshipsof the negotiatingpartiesaswell as means of manipulating he parties'utilityestimates.In addition, previous negotiations are a source of heuristic advice in the restrtucturingask. Therestructuringapproach has been implemented in the PERSUADER, a computer program thatacts as a labor mediator in labor management disputes. To achieve its task, the PERSUADERnegotiates separately with each party, company and union, to guide them in reaching agreement.(NEGOTIATION; PROBLEM RESTRUCTURING; PERSUASIVE ARGUMENTATION;CASE-BASED REASONING; AGENT MODELING; BELIEFREPRESENTATION)

1. IntroductionDuring negotiations, participants must shift their positions (e.g., make concessions)in orderto reachan agreement. Decision theoretic approaches(e.g., Shakun 1988, Gupta1989) formulate concession making as a sequential decision process where the next de-cision of a party depends on the current state, the magnitude of concessions alreadymade, and anticipated responses of the other party(ies). The structureof a negotiationproblem can be expressed in terms of variables denoting negotiation goals and issues,relations and constraints among the variables and reservation prices that denote theminimum acceptable levels at which constraints can be satisfied.'The negotiationprocessis an iterativesearchforappropriatechangesin the goalsand constraintsof the participantsin order to achieve resolutions that are members of a changingjoint solution set (whichinitially may be empty). The final agreed upon solution is a settlement with values forthe negotiation issues, so that the participants'goals are satisfied at some aspirationlevel,and so that constraints are not violated.It is a fact of life in negotiations that deadlocks occur. One way to remove deadlocksis to restructutrehe problem. Problem restructurings the processof dynamically changing

the structure of the negotiation problem to achieve movement towards agreement. Ingeneral, some type of restructuring s necessarywhen one of the partiesrefuses to accepta proposed settlement. Although the whole process of concession making can be viewedas a (trivial) type of restructuring,n the sense that a concession changesthe valule ssignedto a variable, in this paper we reserve the use of the terms "restructuring"and "refor-mulation" for changes in the variables themselves that result in changes in the structureof the negotiation problem.This paper focuses on the restructuring processes that are implemented in the PER-SUADER computer program (Sycara 1987). The PERSUADER simulates hypotheticallabor-managementnegotiations.The system integratesArtificialIntelligence(Al) concepts* Accepted by Kalyan Chatterjee,Gregory Kersten and Melvin F. Shakun, acting as Special Editors. Thispaperwas received February 1990; revision received October 1990.' In the literature (e.g., Shakun 1988, Keeney 1976) a distinction has been drawn between issues, calledoperationalgoals, and beliefs and desires,callednonoperationalgoals. Since both goal categories may be subjectsof restructuring, n the PERSUADER, they are uniformly structured n terms of goailgraphls (see ?4.2) and areuniformly treatedby the restructuringprocesses. Accordingly, we adopt the word "goal"to refer to negotiationissues as well as beliefs and desires of the parties.

1248 0025-1909/91/37 10/1248$01.25Copyright (C 1991, The Instituteof Management Sciences

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PROBLEM RESTRUCTURING IN NEGOTIATION 1249and techniques, such as frame-basedrepresentationsand case-basedreasoning(Kolodner,Simpson and Sycara 1985) with graphsearchand use of multi-attributeutilities (Sycara1988) to come up with a methodology and mechanisms to enable intelligent machineagents to automatically compute and propose problem restructuringsduring simulatednegotiations.Automated problem restructuring is in general a computationally explosive process,given the great number of constraints, and goals presentin any given negotiation problem.Therefore,exhaustive searchis in generalimpractical.This necessitatesthe incorporationin the system of mechanisms to focutsthe attention of the problem solver on promisingreformulations. Another characteristicthat compounds the difficulty of restructuringisthe fact that restructuring is a context-sensitive process that, for a given negotiationproblem, also depends on (1) the beliefs and attitudes of the negotiating participants,(2) the negotiation history, and (3) the negotiation context. Hence, the restructuringmethodology should incorporate explicit mechanisms that link these factors to the re-structuring heuristics. In the PERSUADER, these factors are modeled and representedin object-oriented semantic networks that include ISA hierarchies and inheritance. Eachconcept is represented n termsof a set of attributeswhose values can be numeiic, symbolicor another concept.The PERSUADER engages in the following types of problem restructuring: (1) in-troduction of new goals, (2) goal substitution, (3) goal abandonment, and (4) changingthe reservation prices of the negotiating parties.In order to be able to deal with the complexities of restructuring, the PERSUADERemploys the following restructuringmethods:

1. Case-Based Reasoning (CBR), which consists of retrieving from memory andadapting previous compromises of similar disputants (Kolodner, Simpson and Sycara1985, Sycara 1987). Because negotiation histories and salient information (see ?3) ofthe negotiating process through which the partiesreached agreement is included in eachpast case, a reasoner has access to past reformulations as well as strategies for adaptingprevious cases to produce promising reformulations for the current case.2. SituationAssessmentwhich representsand recognizesnegotiationproblemsin termsof their abstract causal structure. The representational vehicles that are used in situ-ation assessment are called Situational Assessment Packets (SAPs). They embody thecausal knowledge and provide domain independent problem restructuring strategies(Sycara 1987).3. Search of agents' goal graphsto determine interrelationsamongst goals of an agent(Sycara 1987). Since the partiesview the negotiation subjectively in terms of their goalsand desires, by having access to information concerning goals and relationsamong them,a reasoner can produce promising reformulations.4. Persuasiveargumentation,and in particulargeneratingthreats and promises(Sycara1990a). The effect of arguments is to change the beliefs and behavior of the negotiatingparties.In particular,the goal graphsof the partiesarechanged. This restructuringresultsin changing the perception of the parties concerning the negotiation.

Case-basedreasoningcan be used for all types of problemrestructuring.This is possiblesince each previous case includes information about negotiation impasses and the meansby which they were overcome, i.e. the repairsmade to rejected proposals so as to achievemovement towards agreement. Problem restructuring s one type of repairstrategy.As-sociated with each repairof problem restructuring ype is also the restructuringcategory,namely goal introduction, goal substitution, goal abandonment and changing of reser-vation prices. Thus, when a problem solver accesses similar previous impasses, it canselect out of the previous impasses one(s) whose repairsseem most appropriatein thecurrentsituation.In contrastto CBR that accessesand adapts previouslyusedrestructuringstrategies, situation assessment, goal graph search and generation of threats and promisesare generaltivemethods.In other words, they generate reformulations from scratch.

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1250 KATIA P. SYCARA?2 gives a brief summary of the PERSUADER system, presents requirements for prob-lem restructuring and the overall restructuringprocess; ?3 presents an overview of case-based reasoning and how it is used in restructuring; 4 presentsthe generative restructuringprocesses; ?5 presents the generative restructuringprocesses to achieve goal introduction;?6 presents the generative algorithms for goal substitution; ?7 presents the generativealgorithms for goal abandonment and ?8 generative changing of reservation prices. Con-cluding remarksare presented in ?9.

2. The PERSUADER SystemOur model of problem restructuringis part of a general multi-agent, multi-issue ne-gotiation model (Sycara 1987, 1990b) that has been implemented in a computer program,the PERSUADER. In contrast to knowledge-based work on negotiations that has con-centrated on providing support for human negotiators (Kersten et al. 1990, Jarke 1987,Goeltner 1987), our work concentrates on automating the dynamics of the process itself

and coming up with a settlement that the parties agree on. Although the PERSUADERcan operate autonomously, the interfaceallows usersplayingthe role of union and com-pany to registerreactions to the system's suggestions and provide feedback.The PERSUADER system involves three agents: a company, its trade union and themediator whose task is to help the other two agents reach an acceptable compromise.The mediator is engaged in parallel negotiations with the union and company agents.The PERSUADER's input is the set of conflicting goals of the company and the union,and the negotiation context. The negotiation context consists of factors, such as thegeneral state of the economy, the state of the industry to which the company belongs,the financial situation of the company, and the profileof the international union to whichthe local union belongs. The final output is either an agreed upon settlement (contract)or an indication of failure if the negotiating parties did not reach agreement within aparticularnumber of proposals (to simulate the inability of parties in the real world toreach agreement before a strike deadline). A contract consists of a set of issues, such aswages, pensions, provisions for seniority, vacations, etc. and a set of values assigned tothe issues. The final agreed upon contract is the result of iterativecontract modificationby the parties and the mediator.The PERSUADER uses two categoriesof knowledge to perform its tasks: (a) domainknowledge and (b) reasoning knowledge. Domain knowledge includes knowledge aboutnegotiations, negotiators, negotiators' goals, negotiation context and negotiation settle-ments. Each concept is represented in an object-oriented manner using a network offrames and the inheritance mechanism (Sycara 1987). Each frame has slots that representsalient features of the represented concept. The filler of each slot is either a value oranother frame representingan appropriateconcept. For example, the concept of a localunion is represented as a frame that has slots to represent the name of the union (theslot filler is a string denoting the union name), the union leader(the slot filleris a framenetwork representingattributes of the concept of a union leader), the union goals (theslot filler is a goal graph representedas frame network), the international union to whichthis local union belongs (the slot filler is a frame network), the bargaining power of thelocal union (the slot filler is a procedurethat takes as argumentsattributesof the economiccontext and the international union, and returns numerical values), the composition ofthe bargainingunit (the slot filleris a frame network representingthe bargainingunit interms of job classification, number of skilled, unskilled and semiskilled workers, agecategories and degrees of militancy), the time the local has been in the company (theslot filler is a number whose units are months), and the relations of the local with theinternational (the slot filler is a stringthat takes the value "good" or "bad"). For moredetails on the representation, see Sycara (1987). Reasoning knowledge includes theknowledge needed to assess the "fairness"of a solution, and knowledge needed to improvea rejected solution. This knowledge is expressed in terms of multi-attribute utilities as-

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PROBLEM RESTRUCTURING IN NEGOTIATION 1251sociated with the parties' goals, and criteria for selecting negotiation proposals (Sycara1987). To use the system in a new domain, cases should be structuredin terms of thesalient features in the new domain. The reasoning algorithms are domain-independent.Some of the reasoning knowledge that is used in our model has its conceptual originsin standards that are commonly used to justify arbitrationawards (Elkouri and Elkouri1972). The standard that is most frequently used is the prevailing practice standard,namelythe bargainingbehaviorof similarparties.In our work, this standardgets abstractedto reasoningfrom precedentcases. This is a suitablemethod forthe domain since previouscases represent good solutions to the difficulties that are endemic to finding acceptablecompromises in multi-agent negotiations. Knowledge acquisition in the PERSUADERis based on four main sources:( 1) the laborrelations literatureincluding books, journals,newspapersand marazines, (2) published arbitration awards,where the arbitrator citesthe facts and criteria used in the decision, and (3) two human expert mediators,2 and(4) the PERSUADER's Case-Based Reasoning process. Nine months were spent tappingthese sources and making decisions on the knowledge to be initially incorporatedin theCase Knowledge Base. The system is started with a set of cases that are placed in itsKnowledge Base.At the end of each problem solving session the PERSUADER's memoryis updated with information from the newly resolved case as well as any new informationthat has been acquired during problem solving (e.g., from the parties' feedback). Thus,knowledge acquisition and learningis ongoing since it is a by-product of problem solving.The negotiation process consists of iteration and interleaving of three main tasks:generation of a proposal, generation of a counterproposal based on feedback from adissenting party, and persuasiveargumentation.These tasks can be iteratedand interleavedseveral times during negotiation. The mediator agent in the PERSUADER system gen-erates an initial compromise proposal and presents it to both the union and companyagents who evaluate the proposal from their perspectives and give the mediator theirreaction. If both accept the proposal, then it is the final compromise. If one of the agentsrejectsit, the mediator enters a negotiation with that party and makes a decision whetherto change the proposal, or attempt to change the disagreeing party's position.Restructuringtakes place as a result of an explicit rejection by one of the parties andmay result in changing all concerned parties' perceptions regardingthe negotiation. Asuccessful problem restructuringshould at least change the perception of the partywhosedisagreement hinders progresstowards resolution. The desired outcome of problem re-structuring s a new proposalthat givesthe rejectingpartya higher payoffthan the rejectedproposal but does not lowerthe payoffof the partythat had acceptedthe previousproposalto such an extent that it will reject the new proposal.2.1. Requtirementsor Problem Restructutring

The restructuringtask is knowledge- and search-intensive. Sources of restructuringknowledge can be found in the abstract causal structure of a negotiation problem (see?4.1 ), in relationships among the negotiating parties, in beliefs and desires of the nego-tiators and in relationships between the negotiation and the environment. In order toautomate restructuring,this knowledge must be capturedand representedin knowledgestructures explicitly and in a principled way. Unlike rule-basedsystems that use the ruleformalism as a sole representational vehicle, the PERSUADER integrates a variety ofrepresentationalmechanisms for knowledge structuringand problem restructuring: ( I )Situational Assessment Packets (SAPs) that capture the abstract causal structure of anegotiation problem and store general and specific strategiesfor restructuring and reso-lution, (2) Negotiation Cases that capture specific instances of negotiations, (3) GoalGraphs that representgoals/issues, as well as beliefs and desires of the participants, (4)

2 One is a Professorof Economics and the other came up through the ranksof the InternationalMachinists'Union.

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1252 KATIA P. SYCARAUtilities associated with the issues under negotiation and with higher level goals of theparties,and (5) Rules that facilitateinferences. This representationalsynergyis necessaryto enable the system to reason at a deeper level of understanding.We have identifiedsome characteristicsof the task thatgive riseto a set of requirementsfor automated problem restructuring.* The number of variablesthat could enter the restructuringprocess is very largeandnot easy to identify in general. In order that a reasoner produce an effective formulation,it needs to be able to representand maintain sets of possible goals of the agents it isinteractingwith.* Because the set of goals of an agent could be large, and because different types ofreformulation are appropriateunder differentcircumstances, a reasoner must be able tofocuis its attention on promising reformulations in terms of (a) type of restructuring(change of reservation prices, goal abandonment, goal substitution, or introduction of anew goal), and (b) the specific goal(s) that must be introduced or abandoned.* A particularrestructuringmay or may not be able to resolve a deadlock. Based onthe parties' feedback, a reasoner must be able to update its knowledge and inkferencesconcerning the goals of the parties.The input to the restructuringprocess, depicted in Figure 2-1, is a rejected proposal3(the contract issues and their values), the rejected issue and the reason for rejectionprovided by the rejectingparty. These provide focal points for the PERSUADER, fromwhich search for promising reformulationswill be conducted. We make the assumptionthat a partyrejectsa proposal if it does not give it high enough payoff. So, a reformulatorshould look for reformulationsthat result in new proposalswith increased payofffor therejectingparty.On the other hand, the proposalthat resulted from a reformulationshouldnot inordinately decreasethe payoffof the party that had acceptedthe previous proposal.The criterionthat the PERSUADER uses is that a restructuringshould resultin proposalsthat increase the rejecting party's payoff by a greater amount than they decrease thepayoff of the party that had previously accepted the proposal.The first restructuringstrategythe PERSUADER uses is to introduce a new goal inthe negotiations. The new goal should be such that it compensates for some loss of payofffor the rejecting party without appreciablydecreasingthe payoff of the accepting party.Introduction of a new goal is tried first because we believe that it is the mildest form ofreformulation, not requiring abandonment of parties' goals. Introduction of new goalscan be achieved by the restructuringprocesses of case-basedreasoning,goal graphsearchor situation assessment. At each iteration, the PERSUADER attempts to introduce agoal that could result in a promising reformulation. If all the promising reformulationshave been exhausted without breakingthe deadlock, then goal substitution is attempted.The PERSUADER attempts to substitute a suitable goal for an issue/goal that has beenobjected to. Goal substitution can be seen as a relaxation of a party'sdemands that givesthe party lower payoff. Goal substitution is accomplished through goal graphsearch andcase based reasoning. If goal substitution fails to resolve the deadlock, the PERSUADERpursues goal abandonment of the objectionable issue/goal. The process through whichgoal abandonment is achieved is the generation of threats and promises, or case-basedreasoningwhere a previouslyused threat/ promise is retrievedand adaptedto the currentsituation. If goal abandonment also fails to resolve the deadlock, then the PERSUADERpursues change in the reservation price of the rejecting party. This is accomplished bygenerating threats to break off negotiations, or retrievingappropriatenegotiation breakoff threats through case-based reasoning.Since case-based reasoning can be used for every category of problem restructuring,we devote the next section to a brief overview of case-based reasoning and description

3See ?3 for a description of case-basedgeneration of proposals.

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PROBLEM RESTRUCTURING IN NEGOTIATION 1253

e ecteIssue andReason

Goal _ GoalIntroduction Grapht \

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1254 KATIA P. SYCARAjection), the rejection reason (if one is offered) and the PERSUADER's repairs o improvea rejected proposal. Successes are indexed under salient domain features, such as industiyto which the disputant company belongs, geographical location of the company, jobclassification of the employees etc. Impasses have three additional indices, an index in-dicating "failure," he failure cause, and the negotiationissue(s) that was (were) involved.As the PERSUADER settles an increasingnumber of negotiations, its case base is enriched,making available a great varietyof previous cases it can reason from.Cases are organizedin memory hierarchicallyaround important concepts in the prob-lem domain. In order to perform Case-Based Reasoning, cases need to be retrieved interms of conceptual similarity. The basic idea behind conceptual similarity between twoconcepts is that they have important common attributes. For example two truck com-panies are similar because they share the common attributes of being a company andhaving transportation of goods as their product. Similar concepts are organized intolarger groupings based on their similarities, and differentiated from each other in termsof their differences. The two truck companies of the example are organized under themore general concept of "ground transportationcompanies" and differentiated by suchdifferences as location, size, financial condition etc. The high level knowledge structurethat we use to organize similar concepts in memory is called a generalized episode (Ko-lodner 1984). Generalized episodes organize cases into a hierarchical network whosenodes are either another generalized episode or an individual case.The PERSUADER uses CBR to perform a variety of tasks. For each of these tasks, aseparate part of a case is used to guide the reasoning. For example, in generating aninitial compromise, the system reasons from previoussettlements; n generatingpersuasivearguments, it uses previous arguments;in performingproblem restructuring, t uses pre-vious negotiation impasses. Although different knowledge is used in each of these situ-ations, the Case-Based Reasoning algorithm is the same.The steps of the algorithm are as follows: ( 1) Retrieve similar cases from the CaseMemory,4 (2) Determine the case that is most similar to the current negotiation (thebest case), (3) Extractknowledge from the best case, (4) Construct a baseline solution(called the "ballpark" solution), (5) Adapt the baseline solution to fit current circum-stances. At the end of problem solving, memory is updated with the new, successful orfailed, case.To generate an initial settlement, knowledge is extracted from the contract of the mostsimilar precedent case and adjusted through standardadjustments to form the baselinesolution. After further checking and adaptation to fit as closely as possible the charac-teristics of the current negotiation, the adapted solution is proposed to the parties. Formore details of the use of CBR in generating proposals, see Sycara ( 1990b).3.1. Problem Restructuring Using CBR

Each objectionable issue and reason that the rejecting party offers are used as indicesin the case memory to select impasses with the same stated impasse goal and impassecause as in the present deadlock. Examples of reasons for rejection are inability on thepartof the company to pay for a proposed economic demand, consideration of a conces-sion as too low by the union, consideration by the company of a proposed strictseniorityclause as restrictionof its management rights.The selected impasse supplies a repairthatcan facilitate impasse resolution. We have identified severalgeneral categoriesof repairs,such as changing the value of an issue, restructuringthe problem, passing costs of asettlement to thirdparties (e.g., the consumer), invoking authority, extending the currentagreement and resortingto binding arbitration. These repair types are organized in ab-straction hierarchiesin a frame-basedrepresentation.Figure 3-1 depicts part of such anabstraction hierarchy.

4By "cases" we mean appropriatecases or parts of cases, such as a previous argument.

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PROBLEM RESTRUCTURING IN NEGOTIATION 1255Repair

Is-a Is-a is-a

Problem Restructurin Extend Agreement Pass-cost-third-partys-a sa s-a s-a \Is-a

Goal-substitution Goal-abandoment Pass-cost-consumer Gov t-subsidyGoa 1- introduct in Change-reservat i on

FIGURE 3-1. Partial Abstraction Hierarchy of Repairs.

Goal introduction, goal substitution, goal abandonment and changing of reservationprices are refinements of the repair of type "problem restructuring".Information aboutthe various repair types and their refinements is kept as part of the repairs associatedwith cases in memory. The PERSUADER can check and select suitable repair types atthe appropriate time during problem solving.The process of problem restructuringusing case-based reasoning is as follows:51. Construct a memory probe consisting of the conjunction of indication "FAILURE",the rejecting party, the rejected issue and cause for rejection.2. Using the probe retrieve similar failures (impasses).3. Use additional similarity criteria, such as industry to which the company belongs,geographical location, job classifications, dispute context etc. to select the most similarset of impasses to reason from.4. Out of the set of impasses identified in step 3, select those whose repairsare of type"problem restructuring".Access the repairs.5. Out of the repairsidentified in step 4, do:o Select the repairsthat are of type "X".6* Rank order the selected repairsin terms of applicabilityto the current case.* Successively propose the repairsto the rejecting partyin an attempt to resolve theimpasse. If one of the proposed reformulations succeeds in breaking the deadlock,then stop.* If the reformulations of type "X" have been exhausted without success, use gen-erative approaches (see ?4) to construct additional reformulations of type "X".As an example, consider the PERSUADER during deadlocked negotiations of PorterStructuralInc., an airframe manufacturer.One of the important union demands is forjob security. To operationalize this goal, the union had demanded that the companyshould not be allowed to subcontract.The company refusessayingthat a no-subcontractclause restricts its flexibility in decision making. The union insists saying job security isvery important. Deadlock occurs. The case memory is searched for suitable repairs.

Searching memory with index FAILURE, UNION, SUBCONTRACT, JOB-SECURITY7 impasses foundSelect impasses with repair type "restructure"We present the algorithm for the type "goal introduction". The algorithm is the same for all types ofrestructuring.

6 Depending on the point in the restructuringprocess (see Figure 2-1 ) the system is in, the variable X getsinstantiated to "goal-introduction","goal-substitution","goal-abandonment",or "changing-reservation-prices".The algorithm is the same for all types of restructuring.

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1256 KATIA P. SYCARAapplying features similar industry, same area,same job classification3 impasses foundSelect impasses with restructure type "goal introduction"1 impasse found (impasse3)Looking at repair"The company should pay for worker retraining.. ."from impasse3Since retraining costs low relative to company profitsrepair seems applicablePropose that retraininggoal be introducedAlong with the repairs,applicability conditions of the repairs are stored.An additionalcheck is made to determine whether the company can affordretrainingcosts. Retraining

costs are computed for a maximum of 3 of the bargaining unit members for the nextthree years. Costs are compared to the company's projected profits for the next threeyears. Costs are found to be 3%of projected company profits, so retrainingis proposed.The introduction of retraining breaks the deadlock since worker retrainingis an instru-mental goal to the higher level goal of job security and does not restrict the company'sdecision-making flexibility. After further discussion, a lower maximum number of re-trained workers (4 instead of 3 ) is agreed upon and some limitations are also placed onthe current subcontracting language. In other words, once an acceptable restructuringhas taken place, negotiation and concession making may continue for agreement to bereached.4. Overview of Generative RestructuringProcesses

4.1. SitutationAssessmentSituation Assessment is the process throughwhich the PERSUADER handles problemrestructuring n atypicalsituations.In such situations, restructuring s even more importantsince strategiesused in more typical negotiations will probably not work.In order to address typical negotiation situations, an automated reasoner must haveknowledge that allows it to make inferences that result in expectations about the impactof its decisions. In negotiations, we have identified the following sources of expectations:

(a) prevailing behavior of similar agents (prevailing practice), (b) beliefs about the ra-tionality of the agents, (c) beliefs about the temporal continuation of a state, and (d)roles and relationships among the disputants. Departures from typicality, captured inknowledge structures called Situational Assessment Packets (SAPs), take the form ofexpectation violations associated with the above knowledge sources. SAPs that we haveidentified and implemented in the PERSUADER include SAP MISMANAGEMENT,where one negotiating party mismanages a resource necessary for the achievement ofgoals that are common to other parties in the negotiation; SAP IDEOLOGY where aparty refuses some tangible benefits for ideological reasons; SAP MISPLACED-LOY-ALTY wherea partyis pressuredto foregosome benefits to itselfout of loyalty to anotheretc. (for more details on SAPs, see Sycara 1987). SAPs capture knowledge about theabstract causal structure (see Figure 4-2) of negotiations and relate it to violation ofexpectations. Being able to access causal knowledge that it can use to base its inferenceson, enables an automated reasonerto focus its attention on goals that produce promisingreformulations. One of the important kinds of knowledge that SAPs express is the inter-relations among multiple goals, particularlyin atypical situations. The novel solutionsneeded to resolve atypical disputes could not have been found without knowledge ofgoal interrelations (for a detailed example, see ?5.1).SAPs express abstract causal structures of negotiations that transcend particular do-mains. In contrast to cases, the features incorporated in a SAP are features that pertain

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PROBLEM RESTRUCTURING IN NEGOTIATION 1257to the negotiation planning process itself rather than to information about particularnegotiations. In other words, these features contain maeta-planning information (infor-mation to the plannerof how to plan). This has importantconsequences. If two situationscan be recognized in terms of the same SAP, they can be handled by the same meta-planning strategies.Thus, SAPs enable a problem solver to access general advice aboutproblem solutions and utilize solutions from analogous problem situations in differentdomains. The ability to store situations from different domains under the same SAPmakes SAPs very powerful mechanisms. While there may be no precedent in the labormanagement domain, for example, that can help a mediator deal with mismanagementproblems, general experience with mismanagement in other domains can be helpful incoming up with a solution. Organizing similar memories at the abstract level of goalsand plans, as SAPs do, facilitates sharingof information between domains and contextsthat makes finding creative solutions possible. Once an episode has been recognized interms of a SAP, its problem solving heuristics become available for use in situations withdifferent content. Thus, once problem solving advice has been learned in one context, itcan help processing in a different context, if the experience was recognized in terms ofan appropriateSAP.SAPs contain abstract structures that represent:( 1) a problem solving situation, (2)expectations associated with the situation, (3) the reason expectations are violated, (4)who/what is responsible for the violation, (5) strategiesand plans to find an acceptablesolution, and (6) how to justify the solution. Figure4-1 presentsthe conceptual structureof the SAP MISMANAGEMENT.To see how problem restructuring s done, we must firstexamine how various piecesof knowledge and inferences are linked inside a SAP. The causal structure of a SAP is agraph whose nodes represent goals, states and actions of the agents. The nodes of thegraphare connected via severaltypes of links. A link between two goals denotes whetherone goal is instrumental to the other; a link between an action and a goal (or a state)denotes whether the action is a precondition of the goal (or results in the state); a linkbetween two states denotes the relationship between the states; a link between a stateand a goal denotes the causal relationship between the goal and the state (see Fig-ure 4-2).The overallorganizationalstructure nside a SAP is hierarchical rom general to specificknowledge (see Figure 4-2). A hierarchical organization of knowledge within a SAPallows a problemsolver to accessgeneral strategies irstand, dependingon the informationavailable, subsequently access more specific strategiesand plans. Thus, the general strat-egies are at the top of a SAP. Under general strategiesmore specific strategiesare stored.Under those, applicable plans are stored. Once a situation has been recognized as fitting

SAP MISMANAGEMENTrecognition criteria:1. x and v have a noncompetitive high level goal G72. x mismanages some resource, the possession of which is an enablement condition C for theachievement of G.3. G is in dangerof failing

solution: an equitable solution to prevent the failureof G is to have x, the guilty party, bear the brunt ofthe recovery cost by denying him a prerogativeor a rewardjustification: appeal to theme of fairness and add that if Ydoes not perceive the solution as just, then v?willnot cooperate and thus G will fail (which x certainly does not want).FIGURE 4-1. Content of SAP MISMANAGEMENT.

7Thismight seem to be a contradiction in the case of companies and unions. It is not so, however, since thehighest level goal of both company and union is to produce goods for which both get rewarded.

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1258 KATIA P. SYCARAHigher level goal GO shared by agents x and y)

Instrumental goal Instrumental goal

goal G1 contributes to GOsuccess goal G2 contributes to GOsuccess(possessed by agent [xl) (possessed by agent [y])

cause negation of G1

Mismanagement action [x]

goal G3 Fairness goa Interfered by failing GO

plan to achieve goal

Condition: Guilty party knownStrategy: Punish only guilty party

plan specialization

Condition : Party has prerogativePlan: Deny prerogativeFIGURE 4-2. Structureof SAP MISMANAGEMENT.

the structure of a particularSAP, the SAP is accessed. The internal causal structureof aSAP then guides the problem solver in proposing a promising reformulation.4.2. Goal GraphSearchGoal graphs are directed acyclic graphsthat are used as the representationalvehiclesfor modeling parties'goals and beliefs. These models are used as sources of restructuringadvice and as consistency checkers. As will be described in detail in ?5.2 and ?6, goalgraph search is used for goal introduction and goal substitution.8 Goal graphs are notstatic structures. A party's goal graph is updated based on the reaction to problem re-structuring. In this way, during the course of a negotiation an agent's model is refinedand corrected. This functionality is important in automating negotiations since (a) it isnot possible for an agent to have an a priori correct and detailed goal graph of another,

8 The generation of threatsand promises also uses goal graphsearch.

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PROBLEM RESTRUCTURING IN NEGOTIATION 1259PROFITS (+)

PRODUCTION-COST (-) SALES (+)

M-ATERIALS COST /ATERIALS-COST \ QUALITY (+) PRICES (-)PLANT-EFFICIENCY LABOR-COST (-)

EMPLOYEE-SATISFACTION (+)4ECONOMIC-CONCESSIONS EMPLOYMENT (-) ECONOMIC-CONCESSIONS (-)NON-ECONOMIC- 4WAGES ( CONCESSIONS (+) WAGES (-) FRINGES (-)

AUTOMATION )SUBCONTRACT (+)

FIGURE 4-3. A Company's Partial Belief Structure.

and (b) goals are not static but change with external circumstances and an agent's ex-periences. An example of a goal graph is shown in Figure 4-3.9Each node in a goal graphrepresentsone of the agent'sgoals. Arcs in the graphlinkingtwo goals represent the relationshipbetween goals in terms of how one affectspositivelyor negatively the achievement of the other. Associated with each node is:* a sign (+ or -) that denotes the desirabilityof an increase or decrease in that goal.For example, PROFITS(+) representsthe company's goal of increasing its profits.* the amnount y which the goal should be increasedor decreased.The amount's unitscan be either a percentage,an absolute dollar figure,a rangeof values, or a symbol, suchas "a lot". The units chosen depend on the requirements of the domain. We use per-centages and dollar units and the associated meaning of "at least", or "at most" thedenoted amount. The value 0% is used to represent preservationof a goal. For example,

FRINGES(-, A = 5%) indicates that the company desires to decrease the cost of fringebenefits by at least 5%.* the imnportancehat the party attaches to this goal. For example, increasing profitsPROFITS(+, A = 8%,I - 10) means that the company's goal of increasing its profitsby at least 8% has an importance of 10. The importance vaiiable assumes values from 0(least importance) to 10 (greatest importance).* the feasibility, as perceived by the party, of achieving this goal. For example, thefeasibility of achieving an increase in sales SALES(+, A = 6%,I = 9, F = 0.7) has afeasibility of 0.7. Feasibility is a probability measure and takes values from 0 to 1.The nodes at the top of a graph denote an agent's highest level goals. For example,PROFITS(+, A = 8%,I = 10, F = 0.6), representingthe company's desire to increaseits profitsby at least 8%, s the highestlevel goal of the company. The nodes at successivelylower levels denote the subgoalsthroughwhich the higherlevel goals are achieved. Valuesassociated with each of the edges connecting subgoals to goals denote an assessmentabout the percentcontribuition f the subgoalto the accomplishment of the correspondinggoal. The direction of the edges is from subgoalsto the goals to whose achievement theycontribute. Referring back to the highest node in the figure,we see that profits can beraised, (PROFITS(+, A = 8%,1 = 10, F = 0.6)) by decreasing production costs (PRO-9Forease of viewing we draw the goal graphs as trees with only the sign parametershown.

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1260 KATIA P. SYCARADUCTION-COST (-)) or by increasing sales (SALES ( +)). The contribution of a salesincrease to raising profits is 40% and of reducing production costs 60%. The graph isobviously acyclic since it would be absurd to say that a goal contributes to its ownachievement through a series of subgoals.

Contribution ranges from - 100% to 100%. A positive value means that the subgoalsupportsthe achievement of the higherlevel goal. Goal graphs represent nterrelationshipsamong goals in a more detailed fashion, thus subsuming the functionality of AND/ORgraphs. Conjunction is inferred when the sum of the contributions of subgoals is 100%.Disjunction is inferredwhen each subgoal's contribution to the same higher level goal is100%. Allowing negative contributions expands the expressive power of goal graphs. Anegative contribution value has the interpretation that the subgoal not only does notcontribute to the higher level goal but it is detrimental to it. For example, a negativepublic image would have a detrimental effect on a company's sales. A contribution valueof zero means that the subgoal is irrelevant to the achievement of the higher level goal.A path from X to Y in a goal graph constitutes a causal chain that provides an expla-nation of the change in Y in terms of the change in X, assuming no other change hasoccurred in the rest of the graph. The path WAGES(-) to PRODUCTION-COST(-)in the company's goal graph can be interpreted as follows: "Other things being equal,diminishing the cost of wages results in decreasingthe cost of the economic concessions,which causes a decrease in labor costs, leading to a decrease in production costs and anincrease in profits".In addition to an agent's beliefs, the representation ncludes an estimation of his utilities.The concept of utility is the basis for selecting among alternativedecisions. Each alternative

is evaluated in terms of a number of attributes that a decision maker considers important.Utilities express the preference structutre f an agent and the tradeoffs he is willing tomake among various attribute values. The utilities of the individual attributes are com-bined to give the overall utility (payoff) of an alternative. Being able to compare differentalternatives enables a decision maker to choose the alternative that affordshim maximalpayoff. In labor negotiations, the pertinent attributesare the issues under discussion anddifferent contract proposals are the alternative decisions. In the PERSUADER, eachparty's overall payoff is expressedas a linear combination of the utilities associated withthe issues.In order to construct effective reformulations,a reasoner needs to know both the beliefstructure of a party as well as the influence that the environment would have on thebelief structure.In the labordomain, the economic context of a dispute is one of a varietyof environmental factors that influence a company's (union's) belief structure. For ex-ample, in recession, a union's job security goal has higher importance than in boom.When competition is stiff in an industry, a company's automation goal assumes greaterimportance, and also has a greatercontribution towards the goal of reducing productioncosts. In the PERSUADER, knowledge of salient features of the environment is recordedand is reflectedin the shapes of the utility curves and goal importance in the parties' goalgraphs (Sycara 1988). Utility curves arerepresented by the equations that describe them.4.3. Persuasive Argumentation

Persuasiveargumentation s the process through which an agent, the persuacder, ttemptsto change the beliefs and behavior of anotheragent, thepersueadee. n the PERSUADER,the mediator agent is the persuader and the union and company the persuadees. Ourargumentation model has two general methods for generating arguments: (a) constructarguments from scratch, and (b) use case-based reasoning to recall previously used ar-guments and adapt an appropriate one. In our framework, persuasive arguments areviewed as plans used by the persuader problem solver to accomplish his goal. The goalof a mediator is to help the negotiating partiesreach an agreement. This can be facilitatedby increasing the parties' willingness to accept a proposed settlement. We claim that a

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PROBLEM RESTRUCTURING IN NEGOTIATION 1261party'swillingness to accept a proposal is proportional to its perceived payoff. In otherwords, a party rejects a proposal because it does not give it enough payoff. Hence, if apersuadercould manipulate a party's utilities (resulting in manipulation of the party'spayoff), he would be able to affectpredictablythe behavior of the persuadee.Convincinga persuadee to change his evaluation regardinga proposition is modeled as producingan argument to increase the payoff of the proposition. The issues that appearin a prop-osition are a subset of the goals that appear in the agent's belief structure. Hence, thetask of a persuadercan be viewed as finding the most effective argumentthat will changea persuadee'sbelief structurein ways that increase his payoff.Since a persuadee'spayoffcan be approximatedby a linearcombination of his utilities,his payoff can be increased by (1) changing the importance the persuadee attaches to agoal/issue, (2) changing the persuadee'sperception of an issue's value, and (3) pursuinggoal abandonment on the partof the persuadeevia threats/ promises. The PERSUADERgenerates arguments for all three types of desired changes in the beliefs structure of apersuadee (Sycara 1990a). Goal abandonment is one of the ways in which the PER-SUADER performs problem restructuring. ?7 presents details of the restructuringalgorithm.

5. Introductionof New GoalsMovement towards agreement is often facilitatedby the introduction of new goals inthe negotiation. New goals could provide new contexts within which the negotiationcould be perceived. For example, the restructuringof the Southern Airlines negotiation(see ?5.1) through the introduction of the concern of mismanagement and blame attri-

bution (via situation assessment) allows for creative resolution of the negotiation. Intro-duction of new goals could also provide additional ways in which higher-levelgoals canbe achieved, thus compensating for unacceptable aspects of negotiation issues. For ex-ample, the introduction of worker retraining in the Porter Structural Inc. negotiations(?3. 1) compensates somewhat for the detrimental effects of subcontractingto job securityfor the union.In the PERSUADER, besides case-based reasoning, the processes of (1) SituationAssessment, and (2) goal graph search can be used for goal introduction.5. 1. Goal IntrodulctionThroughSituation Assessmnent

EXAMPLE. During contract negotiations, Southern Airlines presents its employeeswith the ultimatum that, if they don't take wage cuts of 8%, the company which hasbecome noncompetitive will go bankrupt.The employees protestand a mediator is calledin. The mediator finds out that Southern Airlines has been losing money because ofmismanagement in an industry where other airlines are making money. The mediatorproposes that the employees accept 5%wage cuts and that the company give stock tothe employees as well as accept employee representativeson the board of directors.10The above example illustratesa situation where the solution to the problem was con-structed neither through adaptation of a case-based solution nor by analyzing utilities,but by introducing a novel alternative. Judging the Southern Airlines negotiations asatypical, the mediator came up with a solution neither in the realm of prevailingpracticenor predictedby payoff adjustments.To distinguish a typical from an atypical situation,the PERSUADER evaluates the presentcase vis a vis prevailingpractice.This evaluationoccurs during applicability checking for knowledge extraction from a selected precedentto construct a ballparksolution. The result of evaluation is an indication of whether thecase can be considered typical or not. If so, adaptation of the ballpark solution takesplace. If not, SituationAssessmentto generatea reformulationof the negotiationproblemis activated.0?Such solutions are not uncommon in realsituations, as is attestedby the 1985 settlement of EasternAirlineswith the International Pilots' Association.

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1262 KATIA P. SYCARATo evaluate case typicality in the above example, the PERSUADER checks that theair transport industry average for wages is 5% ncrease. Asking for a wage cut of 8%, thecompany is far outside the range indicated by prevailing practice. It concludes that thecase is atypical and activates the process of Situation Assessment. Situation Assessment

classifiesatypicalsituations in categoriescharacterizedn termsof the expectation violationthey embody. When an expectationviolation stemming from one of the inferential sources(prevailing behavior of similar agents, role themes, economic rationality, and temporalcontinuation of a state) is encountered, the process of SAP recognition is activated.Example 1 is processed by recognizing that the Southern Airlines negotiation fits SAPMISMANAGEMENT. SAP MISMANAGEMENT is an example of a SAP that is rec-ognized when expectations arisingfrom prevailingbehaviorof similaragentsareviolated.A reasoner would expect a company belonging to a prosperous industry to be makingprofits. The expectation violation involved in each case controls what parts get focusedon. For example, the PERSUADER's knowledge of normality in a company's life allowsit to make the inference that bankruptcy is an abnormal situation. Knowledge of whatbankruptcymeans focuses the attention of the system on the company's finances. Whathas to be examined next is whether bad financial conditions plague many companies inthe industry (as would happen, if, for example, fierce foreign competition caused anindustry slump). Once the reasoner finds out that the present company is the only onein the industry incurring heavy losses, then attention gets focused on discovering thebehavior of the particular company (or union) that caused the bad financial situation.In Example 1, the noncompetitive goal that the company and union share (cf. Figure4-1 ) is to prevent the company from going bankrupt, since that would hurt both thecompany and the union. One characteristicof SAP MISMANAGEMENT is that one ofthe interacting agents is to blame for the danger of the failure of the common goal. Thepotentialfailure is usedas thejustificationfor the proposedsolution,whichwould certainlybe disagreeableto the guilty party.A problem solver using this SAP appealsto the themeof fairness and "just deserts",which is a new goal introduced in the negotiation. Basedon this goal of equity and distributivejustice, a whole new range of solution strategiesare available. These strategies and the solutions they suggest ( 1) are an answer to thenegotiation deadlock, and (2) they could not have been inferred, had the reformulationnot taken place.SAP MISMANAGEMENT introduces the high level goal of "fairness"which changesthe way the parties view the negotiation situation. The company stops perceiving thesituation as one where, because of financial difficulties, it must ask the workers to takeseverewagecuts and expectthe workers o acceptits proposal;sincethe financialdifficultiesof the company are the result of mismanagement, the company must give noneconomiccompensation to offset the loss of worker income. The introduction of the "fairness"goal encourages the union to demand and win noneconomic compensations, such as theright to be represented on the board of directors.In general, SAPs contain not only abstract causal structuresof negotiations that couldbe used for restructuring,but also strategiesand plans for producing concrete proposalsto breakdeadlocks. As can be seen in Figure 4-2, the "Fairness Goal" has associated withit a set of abstractand specific plans, such as "punish only the guilty party" and "denyprerogative". In the Southern Airlines example, the PERSUADER makes use of the"deny prerogative" plan. Since management rights is a kind of prerogative, the PER-SUADER searches the list of management rights for a suitable one (one whose precon-ditions are satisfied in the current negotiation) to negate. This process results in thesuggestion that employee representativesshould sit on the board of directors.5.2. Goal IntrodutctionThrouighGoal Graph Search

An advantage of using goal graph search for introduction of new goals is that thetraversed graph edges provide explicit linkages among goals. These explicit linkages can

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PROBLEM RESTRUCTURING IN NEGOTIATION 1263be presented to the objecting party to change its problem perception in order to increaseits willingness to move towards agreement. Introduction of a new goal is done throughmatching the objectionable goal in the objecting party's goal graph and traversingthegraph upwards (from leaf nodes to their ancestors). Each of these paths shows the con-sequences that a change in the matched goal will have for higher level goals. The idea isto find as appropriate restructuringcandidates those goals whose contribution to higherlevel goals is greater or equal to that of the objectionable goal. The algorithm for intro-ducing a new goal through searchof the belief structureof the partythat has objected toan issue is now presented.Let gi be the objectionable issue causing deadlock.1. Match11 gi in the goal graph.2. Traverse the contribution link to gi's parent goal gk.23. Traverse the links downwards to the set T of children of gk (siblings of gi).4. Out of the set identified in step 3, select the goals whose contribution to gk s greaterthan or equal to the contribution of gi. This set C constitutes the candidates to be in-troduced.5. Delete from C all goals that are already present in the current negotiation.6. Rank order the set C of candidates identified in step 4 in ascending order of con-tribution to gk-.7. Successively introduce the elements of set C in the negotiation in ascending orderof contribution to gk . If one of the elements of C successfullybreaksthe deadlock, STOP.8. If the set of candidates C is unsuccessfully exhausted, check whether gl, is a rootnode. If it is, STOP, else do:

* let gi < gk-* go to step 2.The algorithm identifies a set of candidate goals that get proposed iteratively in anattempt to break the deadlock. The weaker goals, the ones with lower contributions tothe higherlevel goals, areproposed first. The PERSUADER uses the strategyof presentingcandidate goals in terms of increasing strength so as to take into account that the cu-mulative effect of presentinga series of reformulationswill alsobe instrumental n changingthe parties' perceptions. Focus of attention is provided by the rejected goal. The searchstarts with siblings of the rejected goal and expands to searchingfor higher-level goals tointroduce.6. Goal Substitution

Besides case-based reasoning, goal substitution is performed in the PERSUADER bysearchingthe goal graph of the recalcitrantparty.The input to the process is the goal orset of goals that have been the cause of negotiation deadlock. Each rejected goal is usedas a starting point in searchingthe goal graph of the rejecting party. The algorithm forgoal substitution is basically the same as the one for goal introduction.Let gi be the goal causing the current deadlock. The algorithm proceeds as follows:1. Match gi in the goal graph.2. Traverse the contribution link to gi's parent goal gk,.3. Traverse the links downwards to the set T of children of g,, (siblings of gi).4. Out of the set identified in step 3, delete goals that are currently present. Out ofthe remaining goals select the ones whose contribution to gk. s greaterthan or equal tothe contribution of gi. This set constitutes the candidates to be substituted for gi.

" "Match"meansmatching he framerepresentationsf the object nstances. f there is more than oneobjectionable issue, use the algorithm for each one. The objectionable goal can always be found in the goalgraph since it is one of the issues under negotiation.12 gi could have more than one parent goal. If this happens, the algorithmis applied for each of the parents.

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1264 KATIA P. SYCARAThe control strategy the PERSUADER uses for selecting goals to be substituted for giout of the elements of T is to rank order the set of substitution candidates in terms ofcontribution to gk,,delete goals already present and out of the remaining ones, substitutethe goal that has the smallest contribution first.Ifthis substitutiondoes not help eliminate

the deadlock, each of the remaining goals in the candidate set is tried in ascending orderof contribution to g,. If all substitution candidates have been exhausted without success,let gi - g, and repeat the algorithm. The algorithmterminates when g, is a node withno outgoing edges.7. Goal Abandonment

There are two strategies implemented in the PERSUADER that result in goal aban-donment by a party:(a) promise the party the fulfillment of a more important goal if he abandons thecurrent goal,(b) point out that insistence on the current goal threatens a more important goal ofthe party.For example, the promise of higher wages can make a union abandon its goal ofmodification of management's rights clauses (strategy (a)).13 The threat of losing em-ployment can make a union abandon its goal of wage increases (strategy (b)).Which are the goals targeted forabandonment? What is the knowledge and algorithmsthat enable a computer system to automatically generatethreats and promises that resultin abandonment of goals that hinder movement towards agreement? The goals that aretargetedforabandonmentare the issueson which a partyhas refusedto make concessions.The knowledge that the PERSUADER uses is the models of the negotiating parties rep-resented in the goal graphs. Figure 4-3 has shown a partial belief graph of a company.Figure 7-1 depicts a partial belief graph of a union.The processing depends on which partymust be induced to abandongoals. To convincea union to abandon one of its goals using thr-eats, he strategyis to search for companyactions that threaten one of the union's important goals. To convince a company, thestrategy is to discover whether the company's refusal will result in a violation of an

UNION-PRESTIGE (+)

MGT-RIGHTS (-) UNION-SECURITY (+)EMPLOYEE-SATISFACTION (+)

EMPLOYMENT (+)NON-ECONOMIC (+) ECONOMIC (+)

SENIORITY (+) SUBCONTRACT (-) WAGES (+) FRINGES (+)JOB-SECURITY (+)

FIGURE 7-1. Partial Belief Structureof a Union.

13 The Coors Beer company has used this tack with their nonunion employees to avoid weakeningmanagementrights;

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PROBLEM RESTRUCTURING IN NEGOTIATION 1265important company goal. To convince a union to abandon a goal using promises thealgorithm is similar to the one for threats except that instead of finding a more importantpersuadee goal that is violated, the algorithm searches for a more important persuadeegoal that is desired. A goal is violated by an action if the action opposes its sign. Forexample, if the company lays off employees, a reduction in employment, EMPLOY-MENT(-), occurs, violating the union's goal EMPLOYMENT(-+). Since the companycontrolsthe hirings, firingsand concessions, both of these strategiesrequirea goal directedsearch of the company s goal graph. Company goal graph searchpr-oduices set of po-tentially appropriate threats. Search of the union's goal graph is used for selectionlofappropriate threats out of the generated set. In general, if one party controls the contin-gencies, then its own goal graph needs to be searched to generate threatening arguments.Let us assume that party-2 controls the contingencies and party- does not.The algorithm to produce a threat to convince party- to abandon issue X ( *) (where* denotes a (+) or a (-) in the parties' goal graphs) is as follows:141. Find out which of party-2's goals are violated by party-I's refusal. This is done byfollowing the contribution links startingwithX(NOT*) in party-2 goal graph,i.e., tracingthe consequences for party-2 of the negation of its goal. The effects of negating X arepropagated by changing the signs of X's ancestor goals along the path.2. Find out what compensating actions party-2 might carry out to offset the effects ofnegating its goal X. This is done by considering the subgoals ZI, * * *Z, of each goalYfound in step 1. To qualify as a threatening argument, a potential compensating actionZi has to satisfy three conditions: (a) it must be controllable by party-2, (b) it mustviolate a goal of party-I and (c) the importance for party- of this violated goal must begreater than the importance of the demand under discussion. If the third condition isnot satisfied by Zi, its subgoals are checked to see whether they satisfy conditions (a) to(c); otherwise,the subgraph consisting of Zi and all of its contributing subgoalsis pruned,and the sibling goals of Zi are considered in the same way. If some Z,, proves suitable, apotential argument has been found. Whether or not an argument has been generated,steps I and 2 are repeated startingfrom Y and generatinga set of potential arguments.The algorithm at worst visits all nodes in the graph in a Depth-First fashion. Visitednodes are marked, so they are not revisited. The complexity of Depth First Search isO(j El), linear in the number IEl of edges (Even 1979).Generating an argument to convince party-2 about issue X is similar: the X(NOT *)path is followed in party-2's goal graph. The deleterious results that X(NOT*) has onone of its higher level goals are pointed out to party-2.The algorithm to produce a promise to convince a persuadee to abandon a goal issimilar to the algorithmforproducingthreats.The difference lies in step 2(a). To qualifyas a promise, a compensating action Zi, instead of violating a goal of the persuadee, hasto be desired by the persuadee, i.e., have a (+-) sign in the persuadee'sbelief structure.Moreover, in step 2, there is an additional condition (d) that a potential compensatingaction Zi must satisfy: (d) the cost to the persuaderof effecting the promised goal mustbe less than the cost of the abandoned goal.

When the argument-generatingprocess described above produces more than one po-tential threat, the best order of presentation must be chosen. One strategy is to try the"weakest" argument first, presenting "strong" arguments only if the weaker ones fail.This requiresmeans of ranking arguments according to their "convincing" power (Sycara1990a). The ranking follows the order of importance of the goals that the argumentsthreaten. In particular,the importance of the goals of a company (union) depends on14Forclarityof presentation, epresenthealgorithmsn termsof twoparties. fmorethan one partyhasrejected a proposal, conditions (b) and (c) of argument acceptabilitybecome: (b) it must violate goals of allrejecting parties, and (c) the importance for eachl rejecting party of the violated goal must be greater than theimportance of the demand under discussion.

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1266 KATIA P. SYCARAthe financial situation of the company, the state of the industry, the labor supply andthe general economic climate. For example, the goal of reducing labor cost is moreimportant for a company in an industry with high labor cost; if there is abundant laborsupply in an area, the goal of employment is stronger for a union in that area. In thiscase, a threat of layoffs has the greatest convincing power for the union.Consider a negotiation between a company and its union, where the PERSUADERhas suggested a compromise. The company has agreedsaying that the increase in fringebenefits (fringes) is the highest it can afford.The union wants a higherincrease. Deadlockoccurs. The PERSUADER restructuresthe problem by attempting to make the unionabandon the goal of higher increase in fringes. This is done by producing the threat"If the company is forced to grant higher increases in fringes, then it will decrease em-ployment".To generate the above argument, the PERSUADER finds out which company goalsare violated by the union's refusal. Then, it finds out what compensating actions thecompany might use in retaliation. To do this, the PERSUADER matches the fringesgoal in the company's belief graph (see Figure 4-3). It propagatesthe increase in fringesthat the union wants to enforce to the ancestors of the fringes goal (ECONOMIC-CONCESSIONS,LABOR-COST,PRODUCTION-COST, PROFITS). Childrenof theseancestors (e.g., WAGES, EMPLOYMENT) might indicate subgoals that the companycan fulfill to counteract the increase. Such a counteracting action (e.g., EMPLOY-MENT(-)) that violates a union goal (EMPLOYMENT(+)) (see Figure 7-1) that ismore important than the increase in fringes constitutes a threat that is aimed at makingthe union abandon the goal of furtherincreases in fringes.

8. ChangingReservation PricesIf other restructuringmethods have failed, the PERSUADER attempts to change thereservation price of the objecting party. Changing reservation prices is difficult since itinvolves changingnot simply the payoffof a proposedsettlement but changingthe thresh-old of acceptability itself. Besides using case-based reasoning for this task, changing res-ervation prices is performed through the generation of threats to break off negotiationsif the partydoes not accept the current proposal. Breakoffarguments assert that the costof breaking off negotiations is greaterthan the loss in payoff associated with the current

(unacceptable to the rejecting party) proposed settlement. The effectiveness of thesethreats reflects actual labor negotiations (e.g., Herman and Kuhn 1981) where it is ob-served that as the strike deadline approaches, and as the parties calculate the costs of astrikeagainstthe possibleworth of a settlement,theirwillingnessto compromise increases,or equivalently, the payoff requiredfor agreement decreases.To calculate the loss in payoff of the current unacceptableproposal, the PERSUADERuses a heuristic acceptability threshold of 70%payoff for each of the parties. In otherwords, it is assumed that a partywill accept a proposed settlement if it gives payoff (equaland/or) higherthan 70%.The loss in payoff is the difference between 70%and the payoffof the current unacceptable proposal. The loss in payoff also representsthe amount bywhich the reservation price of the rejecting party needs to be changed so that the partywill agree to the proposed settlement. In the current implementation, it is assumed thatloss of payoff is proportionalto the party's breakoff costs. In other words, the greater thenegotiation breakoffcost, the greaterthe payoff loss the party can tolerate (the less theneeded payoff of an acceptable proposal). In the labor negotiations domain, breakoffcosts are strike and lockout costs. To calculate breakoff costs for the union and thecompany, the factors taken into consideration include: the inventory situation of thecompany, the economic conditions in the industry, outstanding orders, the condition of

15This was suggested by our two domain experts.

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PROBLEM RESTRUCTURING IN NEGOTIATION 1267the union's treasury,unemployment in the job classificationsof the bargaining unit andthe strike history of the union. For a target reservationprice change, the PERSUADERcalculates breakoffcost and checks to see whether it is greaterthan the targeted change.If it is, this calculation forms the basis for a negotiation breakoffargument. If it is not,the PERSUADER seeks to see what assumptions would increase the breakoff cost andthe breakoffarguments include these assumptions. For a detailed discussion of breakoffarguments, see Sycara ( 1987).In certain situations, such as labor negotiations, the breakoffcost is a function of time.In such domains, a persuaderhas to convince the rejecting party that negotiations willnot be resumed for as long a time as is needed for the negotiation breakoffcost to yieldthe targeted payoff drop. In the PERSUADER this length of time is looked up from thecurve of strike cost vs time forthe rejectingparty.This curve is approximatedby accessingexperiences with similar parties. The shape of a company's curve depends on the kindof product the company produces. For example, if the grape pickers go on strike at thetime the grapesare ripe, there is an initial period of a few days where the strike cost riseslinearly with time (assuming the strike startedjust before the optimal picking time).After the grapes are overripe, the strike cost drops to zero. For the union, the curve ofstrike cost vs time depends on the shape the union's strike fund is in, the level of unem-ployment for the skills of the union members, and the level of unemployment benefits.

9. ConcludingRemarksNegotiation is a dynamic processwhere the interactions among the partieschange the

space of feasible solutions. A crucial aspect of negotiations, especially in distributivenegotiations where the parties do not in general share goals, is problem restructuringtogenerate a new problem representation. The problem restructuring process facilitatesexpansion of the space of feasible settlements and the generation of possibly commonlyheld goals, thus unblocking negotiations. Restructuringis a highly creative process thatdepends on the experience and insights of the negotiators. It is also nondeterministicsince it must take into consideration the constantly evolving negotiation context. Au-tomating the restructuringprocess is a challengingtask that explores the limits of currentAl technology. We have presented a frameworkand mechanisms to effect computerizedproblem restructuring n negotiations. The presentedalgorithmshave been implementedin the PERSUADER, a computer programthat acts as an automated labor mediator inhypothetical negotiations. The restructuring processes the PERSUADER uses are: ( 1)case-based reasoning, (2) situation assessment, (3) goal graph search and (4) persuasiveargumentation (in particular generating threats and promises). Although the PER-SUADER uses knowledge from the domain of labor relations, the restructuringprocessand algorithms are domain independent.'6

16This researchwas funded in part by the Army ResearchOffice under contract No. DAAG 29-85-K-00230.References

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