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Feasibility and individual rationality in two-person Bayesian games

Listed author(s):
  • Francoise Forges

    ()

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS - Centre National de la Recherche Scientifique - Université Paris-Dauphine)

  • Ulrich Horst

    ()

    (Department of Mathematics - Humboldt Universität zu Berlin [Berlin])

  • Antoine Salomon

    ()

    (LEDa - Laboratoire d'Economie de Dauphine - Université Paris-Dauphine)

Abstract We define feasible, posterior individually rational solutions for two-person Bayesian games with a single informed player. Such a solution can be achieved by direct signalling from the informed player and requires approval of both players after the signal has been sent. Without further assumptions on the Bayesian game, a solution does not necessarily exist. We show that, if the uninformed player has a “uniform punishment strategy” against the informed one, the existence of a solution follows from the existence of Nash equilibrium in infinitely repeated games with lack of information on one side. We also consider the extension of the result when both players have private information.

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Paper provided by HAL in its series Post-Print with number hal-01252950.

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Date of creation: 2015
Publication status: Published in International Journal of Game Theory, Springer Verlag, 2015
Handle: RePEc:hal:journl:hal-01252950
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01252950
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. Michael Peters & Balázs Szentes, 2012. "Definable and Contractible Contracts," Econometrica, Econometric Society, vol. 80(1), pages 363-411, 01.
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  3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476.
  4. Tennenholtz, Moshe, 2004. "Program equilibrium," Games and Economic Behavior, Elsevier, vol. 49(2), pages 363-373, November.
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  6. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
  7. Francoise Forges, 2013. "A folk theorem for Bayesian games with commitment," Post-Print hal-01252953, HAL.
  8. Celik, Gorkem & Peters, Michael, 2011. "Equilibrium rejection of a mechanism," Games and Economic Behavior, Elsevier, vol. 73(2), pages 375-387.
  9. Jérôme Renault, 2001. "3-player repeated games with lack of information on one side," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 221-245.
  10. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
    • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
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  12. Simon, Robert Samuel, 2002. "Separation of joint plan equilibrium payoffs from the min-max functions," Games and Economic Behavior, Elsevier, vol. 41(1), pages 79-102, October.
  13. Gorkem Celik & Michael Peters, 2016. "Reciprocal relationships and mechanism design," Canadian Journal of Economics, Canadian Economics Association, vol. 49(1), pages 374-411, February.
  14. Françoise Forges, 1990. "Equilibria with Communication in a Job Market Example," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 375-398.
  15. Forges, Françoise, 2013. "A folk theorem for Bayesian games with commitment," Games and Economic Behavior, Elsevier, vol. 78(C), pages 64-71.
  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.
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