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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. Matthew Jackson, 2009. "Non-existence of equilibrium in Vickrey, second-price, and English auctions," Review of Economic Design, Springer, vol. 13(1), pages 137-145, April.
    2. Simon, Leo K. & Zame, William R., 1987. "Discontinous Games and Endogenous Sharing Rules," Department of Economics, Working Paper Series qt8n46v2wv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    3. 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.
    4. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
    5. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
    6. Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Econometric Society 2004 North American Winter Meetings 174, Econometric Society.
    7. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    8. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
    9. 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.
    10. 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.
    11. 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.
    12. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
    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. Carmona, Guilherme, 2008. "An Existence Result for Discontinuous Games," FEUNL Working Paper Series wp530, Universidade Nova de Lisboa, Faculdade de Economia.
    15. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    16. 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.
    17. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
    18. 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.
    19. 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.
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