Ordinary repeated games do not apply to real societies where one can cheat and escape from partners. We formulate a model of endogenous relationships that a player can unilaterally end and start with a randomly assigned new partner with no information flow. Focusing on two-person, two-action Prisoner's Dilemma, we show that the endogenous duration of partnerships generates a significantly different evolutionary stability structure from ordinary random matching games. Monomorphic equilibria require initial trust building, while a polymorphic equilibrium includes earlier cooperators than any strategy in monomorphic equilibria and is thus more efficient. This is due to the non-linearity of average payoffs.

We analyze the problem in which agents have non-public information and are to play an asymmetric information game. The agents may reveal some or all of their information to other agents prior to playing this game. Revelation is via exogenously specified certifiable statements. The equilibria resulting from various revelation strategies are used to determine equilibrium revelation of information. Sufficient conditions are provided for complete revelation of all private information. A number of examples are provided illustrating when revelation will or will not occur in commonly analyzed games.