Each of n players, in an infinitely repeated game, starts with subjective beliefs about his opponents' strategies. If the individual beliefs are compatible with the true strategies chose, then Bayesian updating will lead in the long run to accurate prediction of the future of play of the game....

Two players are about to play a discounted infinitely repeated bimatrix game. Each player knows his own payoff matrix and chooses a strategy which is a best response to some private beliefs over strategies chosen by his opponent. If both players' beliefs contain a grain of truth (each assigns...

We show that any correlation device with rational coefficients can be generated by a mechanism where each player sends a private message to a mediator who in turn makes a public deterministic announcement. Moreover, the mechanism suggested is immunized against individual deviations.

We prove an existence result for games with incomplete information with continuous type spaces under the assumption that players have atomic posteriors. This information structure is an extreme example of the failure of absolute continuity of information, hence our result complements the...