Essentials of Bargaining Theory
This chapter gives an introduction to essential concepts and models of two-person negotiations, i. e. bilateral bargaining theory. The main purpose is to provide necessary preliminaries for the subsequent chapters. However, it is deemed worthwhile to add
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This chapter gives an introduction to essential concepts and models of twoperson negotiations, i. e. bilateral bargaining theory. The main purpose is to provide necessary preliminaries for the subsequent chapters. However, it is deemed worthwhile to add to an already large literature an introduction which aims to combine mathematical precision with particular comprehensibility, and which for the first time presents a comprehensive history of thought that ranges from Edgeworth's work in 1881 to most recent corroborations of classical predictions for bargaining by evolutionary models. Moreover, several results appear in more generality than is common or - to the author's knowledge - for the first time. Recommended other introductions to bargaining theory are Osborne and Rubinstein (1990), Binmore, Osborne, and Rubinstein (1992), and Muthoo (1999). Familiarity with basic game theory is assumed, but the appendix to this book collects all game-theoretic concepts, notation, and results which are used. In the first section, Edgeworth's (1881) seminal formalization of individual and collective rationality in a bargaining situation is presented as well as Zeuthen's (1930) model of concession behaviour under risk and Hicks' (1932) equilibrium of strike resistances. Nash's (1950) axiomatic solution of the bargaining problem is the centerpiece of the subsequent section on cooperative models, which also covers links to the earlier contributions and alternative axiomatic solutions. A section on non-cooperative bargaining theory then deals primarily with the finite and infinite horizon alternating offers models of perfect information pioneered by Stahl (1972) and Rubinstein (1982). The latter's relationship to Nash's axiomatic solution is pointed out. Some main features of models with incomplete information are illustrated briefly. In a section on evolutionary bargaining models it is then demonstrated that very demanding assumptions on players' rationality are not necessary for many predictions. The presentation covers the adaptive play model of Young (1993b), the imitation model of Gale, Binmore, and Samuelson (1995), and the model of finite bargaining automata proposed by Binmore, Piccione, and Samuelson (1998). The concluding section primarily deals with the link between theoretical predictions and observations of human bargaining behaviour in laboratory experiments.
S. Napel, Bilateral Bargaining © Springer-Verlag Berlin Heidelberg 2002
Chapter 1. Essentials of Bargaining Theory
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1.1 Early Formalizations and Models Bilateral exchange is a classical bargaining situation. Two agents, 1 and 2, have initial endowments Xl = (X~, X~) E JR;. and x2 = (xi, x~) E lR~ of two perfectly divisible goods. This defines a payoff combination (11"1 (Xl), 11"2 (x 2)) which describes the status quo in terms of players' individual preferences, represented by utility functions 1I"i. Typically, this status quo can be improved by a (partial) bilateral exchange of goods. But what allocation will be reached if exchange is voluntary, the two agen
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