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On the existence of approximate equilibria and sharing rule solutions in discontinuous games

Author

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  • Bich, Philippe

    () (Paris School of Economics, Centre d'Economie de la Sorbonne UMR 8174, Université Paris I Panthéon/Sorbonne)

  • Laraki, Rida

    () (CNRS, University of Paris Dauphine, Ecole Polytechnique)

Abstract

This paper studies the existence of some known 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, and its recent improvements. 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). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that many competition models with discontinuous preferences have a sharing rule solution.

Suggested Citation

  • Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
  • Handle: RePEc:the:publsh:2081
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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.
    2. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    3. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
    4. Oriol Carbonell-Nicolau & Richard McLean, 2014. "On the existence of Nash equilibrium in Bayesian games," Departmental Working Papers 201402, Rutgers University, Department of Economics.
    5. Paul Rothstein, 2007. "Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(2), pages 335-368, April.
    6. James Andreoni & Yeon-Koo Che & Jinwoo Kim, 2005. "Asymmetric Information about Rivals’ Types in Standard Auctions: An Experiment," Levine's Bibliography 666156000000000474, UCLA Department of Economics.
    7. Ziad, Abderrahmane, 1997. "Pure-Strategy [epsiv]-Nash Equilibrium inn-Person Nonzero-Sum Discontinuous Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 238-249, August.
    8. 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.
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    Cited by:

    1. repec:eee:gamebe:v:111:y:2018:i:c:p:75-84 is not listed on IDEAS
    2. repec:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0118-3 is not listed on IDEAS
    3. repec:eee:jetheo:v:177:y:2018:i:c:p:1-33 is not listed on IDEAS
    4. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    5. repec:eee:gamebe:v:111:y:2018:i:c:p:16-19 is not listed on IDEAS
    6. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.

    More about this item

    Keywords

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

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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