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On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous 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

    New relaxations of the Nash equilibrium concept are shown to exist in any strategic game with discontinuous payoff functions. The new concepts are used (1) to show the equivalence between Reny's better-reply security condition [28] and Simon-Zame's endogenous tie-breaking rule equilibrium concept [32], (2) to obtain conditions for the existence of approximated equilibria in a class of discontinuous games that naturally extends Reny's better-reply secure games, and (3) to show the existence of approximated equilibria in a large family of two-player games that contains all standard models of auctions.

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    Bibliographic Info

    Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00846143.

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    Date of creation: 18 Jul 2013
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    Handle: RePEc:hal:cesptp:hal-00846143

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00846143
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    Related research

    Keywords: Discontinuous games; better-reply security; sharing-rule equilibrium; approximated equilibrium; strategic approximation; auctions; diagonal games.;

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    1. Carmona, Guilherme, 2008. "An Existence Result for Discontinuous Games," FEUNL Working Paper Series, Universidade Nova de Lisboa, Faculdade de Economia wp530, Universidade Nova de Lisboa, Faculdade de Economia.
    2. 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.
    3. Hanming Fang, 2004. "Multidimensional Private Value Auctions," Theory workshop papers, UCLA Department of Economics 121473000000000021, UCLA Department of Economics.
    4. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, Econometric Society, vol. 58(4), pages 861-72, July.
    5. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, Springer, vol. 48(1), pages 17-29, September.
    6. Jackson, Matthew O., 2005. "Non-Existence of Equilibrium in Vickrey, Second-Price, and English Auctions," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1241, California Institute of Technology, Division of the Humanities and Social Sciences.
    7. Nicolas, VIEILLE & Rida, LARAKI & Eilon, SOLAN, 2003. "Continuous-Time Games of Timing," Les Cahiers de Recherche, HEC Paris 773, HEC Paris.
    8. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 81(2), pages 813-824, 03.
    9. 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.
    10. 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.
    11. Simon, Leo K, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(4), pages 569-97, October.
    12. 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.
    13. 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.
    14. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, Springer, vol. 48(1), pages 5-16, September.
    15. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, Springer, vol. 48(1), pages 31-45, September.
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