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Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence


  • Yuichi Yamamoto

    () (Department of Economics, University of Pennsylvania)


This paper proposes and studies a tractable subset of Nash equilibria, belief-free review-strategy equilibria, in repeated games with private monitoring. The payoff set of this class of equilibria is characterized in the limit as the discount factor converges to one for games where players observe statistically independent signals. As an application, we develop a simple sufficient condition for the existence of asymptotically efficient equilibria, and establish a folk theorem for N-player prisoner’s dilemma. All these results are robust to a perturbation of the signal distribution, and hence remain true even under almost-independent monitoring.

Suggested Citation

  • Yuichi Yamamoto, 2012. "Characterizing Belief-Free Review-Strategy Equilibrium Payoffs under ConditionalIndependence," PIER Working Paper Archive 12-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:12-005

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    References listed on IDEAS

    1. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
    2. Joseph E. Harrington & Andrzej Skrzypacz, 2011. "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, American Economic Association, vol. 101(6), pages 2425-2449, October.
    3. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    4. Obara, Ichiro, 2009. "Folk theorem with communication," Journal of Economic Theory, Elsevier, vol. 144(1), pages 120-134, January.
    5. Hitoshi Matsushima, 2004. "Repeated Games with Private Monitoring: Two Players," Econometrica, Econometric Society, vol. 72(3), pages 823-852, May.
    6. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
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    Cited by:

    1. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    2. R. Ghidoni & G. Calzolari & M. Casari, 2017. "Climate Change: Behavioral Responses from Extreme Events and Delayed Damages," Working Papers wp2002, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. repec:pra:mprapa:64485 is not listed on IDEAS
    4. Heller, Yuval, 2017. "Instability of belief-free equilibria," Journal of Economic Theory, Elsevier, vol. 168(C), pages 261-286.
    5. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Chandrasekher, Madhav, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.

    More about this item


    repeated game; private monitoring; conditional independence; belief-free review-strategy equilibrium; prisoner’s dilemma;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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