Social games: Matching and the play of finitely repeated games

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.