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

Author

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  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Rida Laraki

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, X - École polytechnique)

Abstract

This paper studies the existence of equilibrium solution concepts in a large class of economic models with discontinuous payoff functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition (Reny (1999)), and its recent improvements (Barelli and Meneghel (2013); McLennan et al. (2011); Reny (2009, 2011)). We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of approximate equilibria and of sharing rule solutions in pure and mixed strategies (Simon and Zame (1990)). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models have a sharing rule solution.

Suggested Citation

  • Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
    • Handle: RePEc:hal:cesptp:hal-01396183
    DOI: 10.3982/TE2081
    Note: View the original document on HAL open archive server: https://hal.science/hal-01396183
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    Citations

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    Cited by:

    1. Han, Lining & Juarez, Ruben, 2018. "Free intermediation in resource transmission," Games and Economic Behavior, Elsevier, vol. 111(C), pages 75-84.
    2. Philippe Bich & Rida Laraki, 2017. "Externalities in economies with endogenous sharing rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 127-137, October.
    3. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    4. Carmona, Guilherme & Podczeck, Konrad, 2018. "Invariance of the equilibrium set of games with an endogenous sharing rule," Journal of Economic Theory, Elsevier, vol. 177(C), pages 1-33.
    5. Barelli, Paulo & Govindan, Srihari, 0. "Existence of monotone equilibria in large double auctions," Theoretical Economics, Econometric Society.
    6. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    7. János Flesch & Dries Vermeulen & Anna Zseleva, 2021. "Legitimate equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 787-800, December.
    8. Carmona, Guilherme & Podczeck, Konrad, 2018. "The conditions in the existence results for discontinuous games by Reny and by Simon and Zame are incomparable," Games and Economic Behavior, Elsevier, vol. 111(C), pages 16-19.
    9. Duvocelle, Benoit & Mourmans, Niels, 2022. "Contests with discontinuous payoffs," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    10. Bich, Philippe, 2019. "Strategic uncertainty and equilibrium selection in discontinuous games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 786-822.
    11. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.

    More about this item

    Keywords

    Reny equilibrium; approximate equilibrium; timing games; strategic approximation; auctions; Discontinuous games; better-reply security; sharing rules;
    All these keywords.

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