We study environments in which agents are randomly matched to play a Prisoner's Dilemma, and each player observes a few of the partner's past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, weshow that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.

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This paper analyzes the implementation of correlated equilibria that are immune to joint deviations of coalitions by cheap-talk protocols. We construct a cheap-talk protocol that is resistant to deviations of fewer than half the players, and using it, we show that a large set of correlated equilibria can be implemented as Nash equilibria in the extended game with cheap-talk. Furthermore, we demonstrate that in general there is no cheap-talk protocol that is resistant for deviations of half the players.

We develop a framework in which individuals' preferences co-evolve with their abilities to deceive others regarding their preferences and intentions. We show that a pure outcome is stable, essentially if and only if it is an e¢cient Nash equilibrium. All individuals have the same deception ability in such a stable state. In contrast, there are non-pure outcomes in which non-Nash outcomes are played, and di¤erent deception abilities co-exist. We extend our model to study preferences that depend also on the opponent's type.

Various papers have presented folk theorem results for repeated games with private monitoring that rely on belief-free equilibria. I show that these equilibria are not robust against small perturbations in the behavior of potential opponents. Specifically, I show that essentially none of the belief-free equilibria is evolutionarily stable, and that in generic games none of these equilibria is neutrally stable. Moreover, in a large family of games (which includes many public good games), the belief-free equilibria fail to satisfy even a very mild stability refinement.