Instability of belief-free equilibria - Yuval Heller (Bar-Ilan University, Department of Economics, 2017)
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.
Keywords: C73; D82; 330; belief-free equilibrium; evolutionary stability; private monitoring; repeated prisoner's dilemma; communication