Title: Cooperative Game Theory Approaches to Negotiation
Abstract: In this chapter, we present an overview of how negotiation and group decision processes are modeled and analyzed in cooperative game theory. This area of research, typically referred to as cooperative bargaining theory, originated in a seminal paper by J. F. Nash (Econometrica, 18(1):155–162, 1950). There, Nash provided a way of modeling negotiation processes and applied an axiomatic methodology to analyze such models. Nash’s approach to modeling negotiation processes is (i) identifying the set of all alternative agreements, (ii) determining the implications of disagreement, (iii) determining how each negotiator values alternative agreements, as well as the disagreement outcome, and (iv) using the obtained payoff functions to reconstruct the negotiations in the payoff space. The feasible payoff set is the set of all payoff profiles resulting from an agreement and the disagreement point is the payoff profile obtained in case of disagreement. This pair is called a bargaining problem in cooperative game theory. The object of study in cooperative bargaining theory is a (bargaining) rule. It maps each bargaining problem to a payoff profile in the feasible payoff set. Studies on cooperative bargaining theory employ the axiomatic method to evaluate bargaining rules. (A similar methodology is used for social choice and fair division problems, as discussed in the chapters by Klamler and Nurmi, this volume.) An axiom is simply a property of a bargaining rule that the researcher argues to be desirable. A typical study on cooperative bargaining theory considers a set of axioms, motivated by a particular application, and identifies the class of bargaining rules that satisfy them. In this chapter, we review and summarize several such studies. In the first part of the chapter, we present the bargaining model of Nash (Econometrica, 18(1):155–162, 1950). In the second part, we introduce the main bargaining rules and axioms in the literature. Here, we present the seminal characterizations of the Nash rule, the Kalai-Smorodinsky rule, and the Egalitarian rule. We also discuss some well-known rules such as the Utilitarian rule, the Dictatorial rule, the Equal Area rule, and the Perles-Maschler rule. In the third part of the chapter, we discuss strategic issues related to cooperative bargaining, such as the Nash program, implementation of bargaining rules, and games of manipulating bargaining rules (for more on strategic issues, see the chapter by Chatterjee, this volume). In the final part, we present the recent literature on ordinal bargaining rules, that is, rules that do not rely on the assumption that the agents have von Neumann-Morgenstern preferences.
Publication Year: 2010
Publication Date: 2010-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 12
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