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A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games

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  • Philippe Bich

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Rida Laraki

    ()
    (Ecole Polytechnique [Palaiseau] - Ecole Polytechnique, IMJ - Institut de Mathématiques de Jussieu - CNRS : UMR7586 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot)

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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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    Bibliographic Info

    Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00717135.

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    Date of creation: Jun 2012
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    Handle: RePEc:hal:cesptp:halshs-00717135

    Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00717135
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    Related research

    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, Springer, vol. 13(1), pages 137-145, April.
    2. Rida Laraki & Eilon Solan & Nicolas Vieille, 2003. "Continuous-time Games of Timing," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, Springer, vol. 48(1), pages 5-16, September.
    4. Jackson, Matthew O. & Jeroen Swinkels, 2004. "Existence of Equilibrium in Single and Double Private Value Auctions," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1192, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Stephen Morris & Hanming Fang, 2004. "Multidimensional Private Value Auctions," Econometric Society 2004 North American Winter Meetings, Econometric Society 174, Econometric Society.
    6. Kim, Jinwoo & Che, Yeon-Koo, 2004. "Asymmetric information about rivals' types in standard auctions," Games and Economic Behavior, Elsevier, Elsevier, vol. 46(2), pages 383-397, February.
    7. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, Econometric Society, vol. 79(5), pages 1643-1664, 09.
    8. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, Springer, vol. 48(1), pages 17-29, September.
    9. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, Springer, vol. 48(1), pages 31-45, September.
    10. Morgan, Jacqueline & Scalzo, Vincenzo, 2007. "Pseudocontinuous functions and existence of Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 174-183, February.
    11. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 418-443, December.
    12. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, Springer, vol. 31(3), pages 573-585, June.
    13. 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, Econometric Society, vol. 70(5), pages 1711-1740, September.
    14. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, Elsevier, vol. 144(3), pages 1333-1340, May.
    15. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, Econometric Society, vol. 74(6), pages 1715-1721, November.
    16. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1029-1056, September.
    17. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 67(3), pages 439-54, July.
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