Fairness in Repeated Games

Matthew Rabin

No 97-252, Economics Working Papers from University of California at Berkeley

Abstract: In addition to pursuing their material self-interest, people are motivated to help those who are kind to them, and to hurt those who are mean to them. Such social preferences influence behavior most when material stakes are small. Rabin (1993) defin es an outcome reflecting such preferences as fairness equilibrium. This paper applies a version of fairness equilibrium to repeated games. Some fairness-equilibrium outcomes in small-stakes, one-shot games are shown to be fairness-equilibrium outcomes e very period in incremental games, which are finitely repeated games of large overall material stakes but very small per-period stakes. For instance, it is a fairness equilibrium for players to cooperate in every period of the finitely repeated Prisoners' Dilemma with arbitrarily high total payoffs, so long as the per-period material payoffs are small. I consider more generally whether fairness equilibria in small-stakes, one shot games can be the stationary fairness-equilibrium outcomes in incremental g ames, providing sufficient and (approximately equivalent) necessary conditions for this result to hold for all fairness preferences meeting my general assumptions. I also show that outcomes that yield either player below her minmax payoffs (which is ofte n true of fairness equilibria in small-stakes, one-shot games) cannot be stationary fairness-equilibrium outcomes for any fairness preferences meeting the general assumptions in incremental games of sufficiently large overall payoffs.

Date: 1997-01-01
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