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Feasibility and individual rationality in two-person Bayesian games

Listed author(s):
  • Françoise Forges

    ()

    (PSL, Université Paris-Dauphine)

  • Ulrich Horst

    ()

    (Humboldt University Berlin)

  • Antoine Salomon

    ()

    (PSL, 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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File URL: http://link.springer.com/10.1007/s00182-015-0520-8
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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 45 (2016)
Issue (Month): 1 (March)
Pages: 11-36

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Handle: RePEc:spr:jogath:v:45:y:2016:i:1:d:10.1007_s00182-015-0520-8
DOI: 10.1007/s00182-015-0520-8
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  1. 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.
  2. Celik, Gorkem & Peters, Michael, 2011. "Reciprocal Relationships and Mechanism Design," Microeconomics.ca working papers gorkem_celik-2011-19, Vancouver School of Economics, revised 01 Aug 2011.
  3. Francoise Forges & Antoine Salomon, 2014. "Bayesian repeated games and reputation," Working Papers hal-00803919, HAL.
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  5. Celik, Gorkem & Peters, Michael, 2011. "Equilibrium rejection of a mechanism," Games and Economic Behavior, Elsevier, vol. 73(2), pages 375-387.
  6. 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.
  7. 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.
  8. Tennenholtz, Moshe, 2004. "Program equilibrium," Games and Economic Behavior, Elsevier, vol. 49(2), pages 363-373, November.
  9. 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.
  10. repec:dau:papers:123456789/11052 is not listed on IDEAS
  11. Kalai, Adam Tauman & Kalai, Ehud & Lehrer, Ehud & Samet, Dov, 2010. "A commitment folk theorem," Games and Economic Behavior, Elsevier, vol. 69(1), pages 127-137, May.
  12. Michael Peters & Balázs Szentes, 2012. "Definable and Contractible Contracts," Econometrica, Econometric Society, vol. 80(1), pages 363-411, 01.
  13. Francoise Forges, 2013. "A folk theorem for Bayesian games with commitment," Post-Print hal-01252953, HAL.
  14. 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.
  15. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, September.
  16. Forges, Françoise, 2013. "A folk theorem for Bayesian games with commitment," Games and Economic Behavior, Elsevier, vol. 78(C), pages 64-71.
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