PUB - Publikationen an der Universität Bielefeld

The theory of repeated games gives insights to understand and explain how the behavior of agents who have engaged in a long-run relationship differs from those of agents who interact only once. The main message of this theory is that repetition facilitates cooperation. Current models of repeated games assume that at each point in time, each participant predetermines either her action for the next period, or the probability distribution her action will be issued from. This assumption is in contrast with the incomplete and non biding agreements, where participants agree on a collusive path to follow and are silent about the enforcing mechanism. This thesis uses a new model of finitely repeated games with objective ambiguity to show that incomplete contracts are stable. In the considered model, at each point in time of the repeated game, and given the observed history, each player has three kind of possible actions for the next period: pure, mixed or ambiguous. An ambiguous action of a player is a set of lotteries over her set of pure actions in the stage-game. A player can for instance decide to remain silent during some periods of the game, which is equivalent to choosing the whole set of lotteries. I find that remaining silent is an optimal punishment strategy. This implies for instance that at a Nash equilibrium of the finitely repeated game, there is no need to specify the enforcing mechanism. Only the target path matters. Another finding is that adding an infinitesimal level of ambiguity to the classic model of finitely repeated games allows to explain the emergence of cooperation. From a theoretical point of view, this thesis studies a model of finitely repeated game that allows to explain the emergence of cooperation without relaxing the assumptions on the information structure available to players (see Kreps et al. (1982) and Kreps and Wilson (1982)), on the perfectness of the monitoring technology (see Abreu et al. (1990), Aumann et al. (1995)), and on players' rationality (see Neyman (1985), Aumann and Sorin (1989)). Another contribution is the complete folk theorem. It is a full characterization of the limit set of the set of payoffs that are approachable by means of pure strategy subgame perfect Nash equilibria of finite repetitions of an arbitrary normal form game. In contrast with the classic folk theorem, which provides necessary and sucient conditions on the stage-game which ensure that each feasible and individually rational payoff vector of the stage-game is approachable by means of subgame perfect Nash equilibria of the finitely repeated game, the complete folk theorem applies to any compact normal form game, and provides a full characterization of the whole set of payoffs achievable by means of equilibrium strategies of the finitely repeated game.