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Existence of equilibria in discontinuous Bayesian games

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  • He, Wei
  • Yannelis, Nicholas C.

Abstract

We provide easily-verifiable sufficient conditions on the primitives of a Bayesian game to guarantee the existence of a behavioral-strategy Bayes–Nash equilibrium. We allow players' payoff functions to be discontinuous in actions, and illustrate the usefulness of our results via an example of an all-pay auction with general tie-breaking rules which cannot be handled by extant results.

Suggested Citation

  • He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    • Handle: RePEc:eee:jetheo:v:162:y:2016:i:c:p:181-194
    DOI: 10.1016/j.jet.2015.12.009
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    1. Bettina Klose & Dan Kovenock, 2015. "The all-pay auction with complete information and identity-dependent externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 1-19, May.
    2. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    3. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    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. Carmona, Guilherme & Podczeck, Konrad, 2014. "Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 130-178.
    6. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    7. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    8. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
    9. He, Wei & Sun, Xiang, 2014. "On the diffuseness of incomplete information game," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 131-137.
    10. 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.
    11. 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.
    12. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    13. Bagh, Adib, 2010. "Variational convergence: Approximation and existence of equilibria in discontinuous games," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1244-1268, May.
    14. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    15. He, Wei & Yannelis, Nicholas C., 2015. "Discontinuous games with asymmetric information: An extension of Reny's existence theorem," Games and Economic Behavior, Elsevier, vol. 91(C), pages 26-35.
    16. 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.
    17. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    18. 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.
    19. Pavlo Prokopovych, 2013. "The single deviation property in games with discontinuous payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 383-402, June.
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    Cited by:

    1. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    2. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    3. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    4. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    5. Blake A. Allison & Jason J. Lepore, 2024. "Invariant Equilibrium in Discontinuous Bayesian Games," Games, MDPI, vol. 15(3), pages 1-14, May.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Bernard Cornet, 2020. "The Gale–Nikaido–Debreu lemma with discontinuous excess demand," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 169-180, October.
    8. Einy, Ezra & Haimanko, Ori, 2020. "Equilibrium existence in games with a concave Bayesian potential," Games and Economic Behavior, Elsevier, vol. 123(C), pages 288-294.
    9. R. R. Routledge & R. A. Edwards, 2020. "Ambiguity and price competition," Theory and Decision, Springer, vol. 88(2), pages 231-256, March.
    10. Yohan Pelosse, 2024. "A Non-Cooperative Shapley Value Representation of Luce Contests Success Functions," Working Papers 2024-01, Swansea University, School of Management.
    11. 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.
    12. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in contests with bid caps," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    13. Haimanko, Ori, 2024. "Bayesian Nash equilibrium in all-pay auctions with interdependent types," Games and Economic Behavior, Elsevier, vol. 146(C), pages 222-233.
    14. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    15. Wang, Chun & Pi, Jinxiu & Zhou, Die & Tang, Wei & Yang, Guanghui, 2023. "Dynamics of n-person Cournot games with asymmetric information and heterogeneous expectations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    16. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.

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    More about this item

    Keywords

    Discontinuous Bayesian game; Behavioral strategy; Random disjoint payoff matching; Equilibrium existence; All-pay auction;
    All these keywords.

    JEL classification:

    • 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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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