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Belief-free equilibria in games with incomplete information: characterization and existence

  • Lovo, Stefano

    ()

  • Tomala, Tristan

    ()

  • Hörner, Johannes

    ()

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    In this paper, the authors 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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    File URL: http://www.hec.fr/var/fre/storage/original/application/0db41102b0541d8003ce2083e7f50ad5.pdf
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    Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 921.

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    Length: 79 pages
    Date of creation: 10 Oct 2009
    Date of revision:
    Handle: RePEc:ebg:heccah:0921
    Contact details of provider: Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
    Web page: http://www.hec.fr/

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    2. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, 03.
    3. Forges, Françoise, 1992. "Repeated games of incomplete information : non-zero-sum," Economics Papers from University Paris Dauphine 123456789/184, Paris Dauphine University.
    4. Drew Fudenberg & Eric Maskin, 1987. "On the Dispensability of Public Randomization in Discounted Repeated Games," Working papers 467, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Renault, Jérôme & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Economics Papers from University Paris Dauphine 123456789/6103, Paris Dauphine University.
    6. Peski, Marcin, 2008. "Repeated games with incomplete information on one side," Theoretical Economics, Econometric Society, vol. 3(1), March.
    7. Drew Fudenberg & David Levine, 1987. "Reputation and Equilibrium Selection in Games With a Patient Player," Working papers 461, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    9. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    10. Thomas E. Wiseman, 2011. "A Partial Folk Theorem for Games with Private Learning," 2011 Meeting Papers 181, Society for Economic Dynamics.
    11. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. 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.
    13. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Levine's Bibliography 122247000000001569, UCLA Department of Economics.
    14. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, 03.
    15. Horner, Johannes & Lovo, Stefano & Tomala, Tristan, 2009. "Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence," Economics Papers from University Paris Dauphine 123456789/9834, Paris Dauphine University.
    16. Shalev Jonathan, 1994. "Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs," Games and Economic Behavior, Elsevier, vol. 7(2), pages 246-259, September.
    17. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Jérôme Renault, 2001. "3-player repeated games with lack of information on one side," International Journal of Game Theory, Springer, vol. 30(2), pages 221-245.
    19. Israeli, Eitan, 1999. "Sowing Doubt Optimally in Two-Person Repeated Games," Games and Economic Behavior, Elsevier, vol. 28(2), pages 203-216, August.
    20. Forges,F. & Minelli,E., 1995. "Property of Nash Equilibria in Repeated Games with Incomplete Information," Papers 9518, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    21. Thomas, J. P., 1995. "Subgame-perfect attainment of minimax punishments in discounted two-person games," Economics Letters, Elsevier, vol. 47(1), pages 1-4, January.
    22. Renault, Jérôme & Tomala, Tristan, 2004. "Learning the state of nature in repeated games with incomplete information and signals," Economics Papers from University Paris Dauphine 123456789/6115, Paris Dauphine University.
    23. Takahashi, Satoru & Chassang, Sylvain, 2011. "Robustness to incomplete information in repeated games," Theoretical Economics, Econometric Society, vol. 6(1), January.
    24. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
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