Instability of Belief-Free Equilibria

26 Pages Posted: 22 May 2015 Last revised: 5 Jan 2017

Date Written: January 4, 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: Belief-free equilibrium, evolutionary stability, imperfect private monitoring, repeated Prisoner's Dilemma, communication

JEL Classification: C73, D82

Suggested Citation

Heller, Yuval, Instability of Belief-Free Equilibria (January 4, 2017). Journal of Economic Theory, forthcoming, Available at SSRN: or

Yuval Heller (Contact Author)

Bar Ilan University ( email )

Dept. of Economics, Building 504
Bar Ilan University
Ramat Gan, 5290002
+972 5252 82182 (Phone)

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