Division of the Humanities and Social Sciences California Institute of Technology Pasadena, California 91125 Social Games: Matching and the Play of Finitely Repeated Games

We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatis ed with the play of their current partners can join together and play a new equilibrium. This imposes new re nements on equilibrium play, where play depends on the relative populations of players in di erent roles, among other things. We also examine nite repetitions of games where players may choose to rematch in any period. Some equilibria of xed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding xed-player repeated games. We explore existence under di erent equilibrium de nitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiationproof equilibria, and even to be Pareto ineÆcient. JEL classi cation numbers: A14, C71, C72, C78, J41.