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

  • Philippe Bich


    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

  • Rida Laraki


    (Ecole Polytechnique [Palaiseau] - Ecole Polytechnique, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS)

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    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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    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
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    1. 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.
    2. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    3. Hanming Fang & Stephen Morris, 2003. "Multidimensional Private Value Auctions," Cowles Foundation Discussion Papers 1423, Cowles Foundation for Research in Economics, Yale University.
    4. Leo K. Simon and William R. Zame., 1987. "Discontinuous Games and Endogenous Sharing Rules," Economics Working Papers 8756, University of California at Berkeley.
    5. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer, vol. 48(1), pages 5-16, September.
    6. Nicolas, VIEILLE & Rida, LARAKI & Eilon, SOLAN, 2003. "Continuous-Time Games of Timing," Les Cahiers de Recherche 773, HEC Paris.
    7. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 569-597.
    8. 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.
    9. 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.
    10. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer, vol. 48(1), pages 17-29, September.
    11. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer, vol. 48(1), pages 31-45, September.
    12. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, 03.
    13. 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.
    14. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    15. 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.
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