In the classical two players PD game there are two players and each can either cooperate or defect. The key condition is that defection always pays more than cooperation, but mutual cooperation pays more than mutual defection. In this thesis we analyze several n-player, infinitely repeated Prisoner's Dilemma type games in which each player seeks to maximize her long-run average payoff. This extends the work of S. Smale, M. Benaim and M. Hirsch.; We assume that each player uses a stochastic behavior rule based on the average payoffs that all players received in the previous stages. We make the assumption that all the players are rational and wish to maximize their long run average payoff. With this in mind we look at different classes of strategies that attempt to achieve this goal and analyzing them by studying an associated differential equations. In addition we look at games where the players do not have perfect information. This can mean that the players only know the expected payoff function or that the players have access to different information.
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