CIRJE-F-491. Kandori, Michihiro, "Chicken in Prison: Weakly Belief-Free Equilibria in Repeated Games with Private Monitoring", April 2007.

The present paper introduces the notion of weakly belief-free equilibria for repeated games with imperfect private monitoring. This is a tractable class which subsumes, as a special case, the belief-free equilibria, which have played a major role in the existing literature (Ely and Valimaki (2002) and Ely, Horner, and Olszewski (2005)). An example is presented, where a simple weakly belief-free equilibrium outperforms the belief-free equilibria. The present paper also introduces the notion of reduced games of a repeated game and shows that weakly belief-free equilibria admit a recursive structure in the space of reduced games. The example embeds the chicken game, as the reduced games, in the repeated prisoners' dilemma with private monitoring.