Instability of Belief-free Equilibria

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.

JEL Classification: C73, D82.

Keywords: Belief-free equilibrium, evolutionary stability, private monitoring, repeated Prisoner’s Dilemma, communication.