Social games: Matching and the play of finitely repeated games

We examine a new class of games, which we call social games, such that players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play in games, and we show how play depends on the relative populations of players in different roles, among other things. We also introduce finitely repeated social games where players may choose to rematch in any period. Some equilibria of fixed-player finitely repeated games cannot be sustained as equilibria in a finitely repeated social game. Conversely, the set of repeated matching equilibria includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence of finitely repeated matching equilibria, the relationship to renegotiation-proof equilibrium, and show how new predictions are made in trust and centipede games. (C) 2008 Elsevier Inc. All rights reserved.