Instability of belief-free equilibria

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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.

Original languageEnglish
Pages (from-to)261-286
Number of pages26
JournalJournal of Economic Theory
StatePublished - 1 Mar 2017

Bibliographical note

Funding Information:
A previous version of this manuscript was entitled “Instability of Equilibria with Private Monitoring.” I would like to express my deep gratitude to Mehmet Ekmekci, Peter Eso, Michihiro Kandori, Erik Mohlin, Thomas Norman, Ron Peretz, Satoru Takahashi, Jorgen Weibull, Yuichi Yamamoto, the associate editor, and the referees, for many helpful comments. I am grateful to the European Research Council for its financial support (starting grant #677057).

Publisher Copyright:
© 2017 Elsevier Inc.


  • Belief-free equilibrium
  • Communication
  • Evolutionary stability
  • Private monitoring
  • Repeated Prisoner's Dilemma


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