Repetition and cooperation : a model of finitely repeated games with objective ambiguity

In this paper, we present a model of finitely repeated games in which players can strategically make use of objective ambiguity. In each round of a finite rep- etition of a finite stage-game, in addition to the classic pure and mixed actions, players can employ objectively ambiguous actions by using imprecise probabilistic devices such as Ellsberg urns to conceal their intentions. We find that adding an infinitesimal level of ambiguity can be enough to approximate collusive payoffs via subgame perfect equi- librium strategies of the finitely repeated game. Our main theorem states that if each player has many continuation equilibrium payoffs in ambiguous actions, any feasible pay- off vector of the original stage-game that dominates the mixed strategy maxmin payoff vector is (ex-ante and ex-post) approachable by means of subgame perfect equilibrium strategies of the finitely repeated game with discounting. Our condition is also necessary.