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Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence

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We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.

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  • Johannes Horner & Stefano Lovo & Tristan Tomala, 2009. "Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence," Cowles Foundation Discussion Papers 1739, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1739
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    Citations

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    Cited by:

    1. Hörner, Johannes & Takahashi, Satoru & Vieille, Nicolas, 2014. "On the limit perfect public equilibrium payoff set in repeated and stochastic games," Games and Economic Behavior, Elsevier, vol. 85(C), pages 70-83.
    2. Johannes H�rner & Satoru Takahashi & Nicolas Vieille, 2012. "On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games," Working Papers 1397, Princeton University, Department of Economics, Econometric Research Program..
    3. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    4. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    5. repec:eee:jfinec:v:127:y:2018:i:2:p:342-365 is not listed on IDEAS
    6. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2013. "Strategic information exchange," Games and Economic Behavior, Elsevier, vol. 82(C), pages 444-467.
    7. Laclau, M., 2014. "Communication in repeated network games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 87(C), pages 136-160.
    8. Chen, Bo, 2010. "A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring," Journal of Economic Theory, Elsevier, vol. 145(1), pages 402-420, January.
    9. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
    10. 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.
    11. 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.
    12. Joyee Deb & Yuhta Ishii, 2016. "Reputation Building under Uncertain Monitoring," Cowles Foundation Discussion Papers 2042, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Repeated games with incomplete information; Harsanyi doctrine; Belief-free equilibria;

    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

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