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Chapter 5: Bargaining games

Chapter 5: Bargaining games

pp. 89-104

Authors

, George Mason University, Virginia
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Summary

A man has free choice to the extent that he is rational.

Thomas Aquinas

BARGAINING focuses on a possible division of gains from joint action through cooperation between two or more parties. Gains may include a peace dividend from the cessation of violent conflict, new revenue from joint ventures or partnerships, allocation of water in a shared river stream, etc. In bargaining games, a gain from cooperation is often called a surplus. In spite of their common interest in the division of available gains, negotiators often differ over the precise partition, given a desire to attain as large a share of the “pie” as possible. The partition of a surplus constitutes bargaining activity in many negotiations. In this chapter, the principles of bargaining theory are derived from a game theory methodology. Bargaining theories help agents assess the relative value of different offers presented to them and also determine the relative value of their offers to be made to the other during negotiation.

In a two-person bargaining situation, for example, two individuals “have the opportunity to collaborate for mutual benefit in more than one way” whereas each individual has the desire to maximize her gain in bargaining, in solving the joint efficiency problem, bargainers have to search for a mutually beneficial but unique contract that determines “the amount of satisfaction each individual should expect to get from the situation” (Nash 1950, 155). In so doing, we ask such questions as how knowledge about the division, enforceable through a binding agreement, can lead to a reasonable share of the available gain. In this context, we are not so concerned about what people have to do to achieve those payoffs, in contrast with strategic settings where players have to act independently without being able to prearrange each other's actual behavior and its outcome. As will be seen in the section immediately following, this chapter departs from the previous ones, in which deviation from a Pareto optimal solution is derived from a situation in which individual incentives play a prominent role with diverging interests.

In this chapter, bargaining problems are constituted by both a payoff distribution and strategy coordination. In particular, the “rules of a bargaining game” have implications for whether and when an agreement can be reached and, if it can, what the likely division is.

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