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Belief-free Equilibria in games with incomplete information

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  • LOVO, Stefano

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  • HÖRNER, Johanes

    ()

Abstract

In this paper, the authors define belief-free equilibria in two-player games with incomplete information as sequential equilibria for which players’ continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. They characterize a set of payoffs that includes all belief-free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief-free equilibrium payoff.

Suggested Citation

  • LOVO, Stefano & HÖRNER, Johanes, 2006. "Belief-free Equilibria in games with incomplete information," HEC Research Papers Series 845, HEC Paris.
  • Handle: RePEc:ebg:heccah:0845
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    References listed on IDEAS

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    1. Martin W. Cripps & Jonathan P. Thomas, 2003. "Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 433-462, August.
    2. Forges, Francoise & Minelli, Enrico, 1997. "A Property of Nash Equilibria in Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(2), pages 159-175, February.
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    4. Forges, Francoise, 1992. "Repeated games of incomplete information: Non-zero-sum," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 6, pages 155-177 Elsevier.
    5. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 43, pages 1665-1686 Elsevier.
    6. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, March.
    7. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    8. Jeffrey C. Ely & Juuso Välimäki, 2003. "Bad Reputation," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 785-814.
    9. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    10. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
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    Cited by:

    1. Rosenberg, Dinah & Solan, Eilon & Vieille, Nicolas, 2013. "Strategic information exchange," Games and Economic Behavior, Elsevier, vol. 82(C), pages 444-467.
    2. Yuichi Yamamoto, 2014. "We Can Cooperate Even When the Monitoring Structure Will Never Be Known," PIER Working Paper Archive 17-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 08 Apr 2017.
    3. Hörner, Johannes & Lovo, Stefano, 2017. "Belief-free Price Formation," TSE Working Papers 17-790, Toulouse School of Economics (TSE).
    4. 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..
    5. 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.
    6. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Laclau, M., 2014. "Communication in repeated network games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 87(C), pages 136-160.
    8. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    9. Carlsson, Hans & Wichardt, Philipp C., 2012. "On the belief (in-)dependence of sequential equilibria," Economics Letters, Elsevier, vol. 115(3), pages 504-507.
    10. Songzi Du & Haoxiang Zhu, 2014. "Welfare and Optimal Trading Frequency in Dynamic Double Auctions," NBER Working Papers 20588, National Bureau of Economic Research, Inc.
    11. de Clippel, Geoffroy & Eliaz, Kfir & Rozen, Kareen, 2016. "The Silent Treatment," CEPR Discussion Papers 11335, C.E.P.R. Discussion Papers.
    12. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    13. 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.
    14. 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.
    15. Chandrasekher, Madhav, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.
    16. repec:eee:jfinec:v:127:y:2018:i:2:p:342-365 is not listed on IDEAS
    17. repec:eee:gamebe:v:108:y:2018:i:c:p:411-431 is not listed on IDEAS
    18. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    19. Joyee Deb & Yuhta Ishii, 2016. "Reputation Building under Uncertain Monitoring," Cowles Foundation Discussion Papers 2042, Cowles Foundation for Research in Economics, Yale University.
    20. 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.
    21. 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.
    22. 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.

    More about this item

    Keywords

    game theory; equilibria; information;

    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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