CARESS Working Paper #00-16 Belief-Based Equilibria in the Repeated Prisoners ’ Dilemma with Private Monitoring¤

We analyze in…nitely repeated prisoners ’ dilemma games with imper-fect private monitoring, and construct sequential equilibria where strate-gies are measurable with respect to players ’ beliefs regarding their oppo-nents ’ continuation strategies. We show that, when monitoring is almost perfect, the symmetric e¢cient outcome can be approximated in any pris-oners ’ dilemma game, while every individually rational feasible payo ¤ can be approximated in a class of prisoner dilemma games. We also extend the approximate e¢ciency result to n-player prisoners ’ dilemma games and to prisoner’s dilemma games with more general information structure. Our results require that monitoring be su¢ciently accurate but do not require very low discounting.