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On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games

Author

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  • Philippe Bich

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

  • Rida Laraki

    (X - École polytechnique, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper studies the existence of some known equilibrium solution concepts in a large class of economic models with discontinuous payo functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition [34], and its recent improvements [3, 25, 35, 36]. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame [38]). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that in any general equilibrium model with discontinuous preferences, there is a sharing rule solution.

Suggested Citation

  • Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01071678, HAL.
  • Handle: RePEc:hal:cesptp:hal-01071678
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01071678
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    References listed on IDEAS

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    1. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
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    5. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, January.
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    19. 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.
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    Cited by:

    1. Vincenzo Scalzo, 2016. "Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 571-586, March.

    More about this item

    Keywords

    Discontinuous games; better-reply security; sharing rules; approximate equilibrium; Reny equilibrium; strategic approximation; auctions; timing games; exchange economy;

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