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A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games

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    Abstract

    Several relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny's better-reply security condition [Reny, P.J. (1999). On the existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games] to Simon-Zame's endogenous tie-breaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules].

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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2012/12040.pdf
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    Bibliographic Info

    Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12040.

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    Length: 25 pages
    Date of creation: Jun 2012
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    Handle: RePEc:mse:cesdoc:12040

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    Keywords: Discontinuous games; Nash equilibrium; Reny equilibrium; better-reply security; endogenous sharing rule; quasi equilibrium; finite deviation equilibrium; symmetric games.;

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    1. Carmona, Guilherme, 2008. "An Existence Result for Discontinuous Games," FEUNL Working Paper Series wp530, Universidade Nova de Lisboa, Faculdade de Economia.
    2. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    3. Rida Laraki & Eilon Solan & Nicolas Vieille, 2003. "Continuous-time Games of Timing," Discussion Papers 1363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Jackson, Matthew O., 2005. "Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions," Working Papers 1241, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Jackson, Matthew O. & Jeroen Swinkels, 2004. "Existence of Equilibrium in Single and Double Private Value Auctions," Working Papers 1192, California Institute of Technology, Division of the Humanities and Social Sciences.
    6. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
    7. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
    8. Fang, Hanming & Morris, Stephen, 2006. "Multidimensional private value auctions," Journal of Economic Theory, Elsevier, vol. 126(1), pages 1-30, January.
    9. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
    10. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
    11. Kim, Jinwoo & Che, Yeon-Koo, 2004. "Asymmetric information about rivals' types in standard auctions," Games and Economic Behavior, Elsevier, vol. 46(2), pages 383-397, February.
    12. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
    13. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    14. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
    15. Leo K. Simon and William R. Zame., 1987. "Discontinuous Games and Endogenous Sharing Rules," Economics Working Papers 8756, University of California at Berkeley.
    16. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, 09.
    17. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    18. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    19. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
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