Cooperation and computability in n-player games

A Common Interest game is a game that has a unique vector of payoffs that strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such an n-player Common Interest game. We restrict supergame strategies to be computable within Church's thesis, and we introduce computable trembles on these strategies. If the trembles have sufficiently large support, the only equilibrium vector of payoffs that survives is the Pareto-efficient one. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future. The players take turns to reveal their cooperative intentions, and the result is proved by backwards induction on the set of players. We also show that our equilibrium selection result fails when there are a countable infinity of players. © Elsevier Science B.V.