%0 Journal Article
%T Renegotiation Perfection in Infinite Games
%A Julian C. Jamison
%J Game Theory
%D 2014
%R 10.1155/2014/742508
%X We study the dynamic structure of equilibria in game theory. Allowing players in a game the opportunity to renegotiate, or switch to a feasible and Pareto superior equilibrium, can lead to welfare gains. However, in an extensive-form game this can also make it more difficult to enforce punishment strategies, leading to the question of which equilibria are feasible after all. This paper attempts to resolve that question by presenting the first definition of renegotiation-proofness in general games. This new concept, the renegotiation perfect set, satisfies five axioms. The first three axioms¡ªnamely Rationality, Consistency, and Internal Stability¡ªcharacterize weakly renegotiation-proof sets. There is a natural generalized tournament defined on the class of all WRP sets, and the final two axioms¡ªExternal Stability and Optimality¡ªpick a unique ¡°winner¡± from this tournament. The tournament solution concept employed, termed the catalog, is based on Dutta¡¯s minimal covering set and can be applied to many settings other than renegotiation. It is shown that the renegotiation perfection concept is an extension of the standard renegotiation-proof definition for finite games, introduced by (Benoit and Krishna 1993), and that it captures the notion of a strongly renegotiation-proof equilibrium as defined by (Farrell and Maskin 1989). 1. Introduction In sharp contrast with the welfare theorems of general equilibrium theory, traditional equilibrium concepts in game theory exhibit no particular tendency to pick out Pareto efficient outcomes. The various Folk theorems suggest that ¡°coordination¡± may be possible in repeated games but that great many other strategy choices can also be supported as equilibria.1 This result displays an unfortunate lack of predictive power. However, even were it possible to reach an efficient equilibrium in a one-shot game, repeated games pose another quandary: coordination generally requires the threat of punishments, and these are in turn often inefficient by their very nature. Thus if it is always possible to renegotiate to an efficient equilibrium, punishments may no longer be credible and the original equilibrium itself breaks down. Equilibria that are immune to such problems are called renegotiation-proof. The relationship between renegotiation-proofness and Pareto efficiency is exactly analogous to that between subgame perfection and Nash equilibrium: both require credibility of off-path events. The motivation and underlying assumption for the renegotiation literature in game theory is that the group of players as a whole can (and
%U http://www.hindawi.com/journals/gt/2014/742508/