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Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions

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  • Carmona, Guilherme
  • Podczeck, Konrad

Abstract

Balder's (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky (2011) and Barelli and Meneghel (2012) for finite-players games, to games with a measure space of players and establish the existence of pure strategy Nash equilibrium for such games. A specification of our main existence result is provided which is ready to fit the needs of applications. As an illustration, we consider several optimal income tax problems in the spirit of Mirrlees (1971) and use our game-theoretic result to show the existence of an optimal income tax in each of these problems.

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  • Carmona, Guilherme & Podczeck, Konrad, 2013. "Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions," MPRA Paper 44263, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:44263
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    Cited by:

    1. Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers 2013-18, Faculty of Economics and Statistics, Universität Innsbruck.
    2. Barlo, Mehmet & Carmona, Guilherme, 2015. "Strategic behavior in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 134-144.
    3. 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.
    4. Chen, Enxian & Qiao, Lei & Sun, Xiang & Sun, Yeneng, 2022. "Robust perfect equilibrium in large games," Journal of Economic Theory, Elsevier, vol. 201(C).
    5. Kolpin, Van, 2014. "Endogenous convention, prejudice, and trust in demographic summary games," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 128-133.
    6. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    7. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.
    8. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    9. Wu, Bin, 2022. "On pure-strategy Nash equilibria in large games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 305-315.
    10. Guilherme Carmona & Konrad Podczeck, 2016. "Existence of Nash equilibrium in ordinal games with discontinuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 457-478, March.
    11. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    12. 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.
    13. Guilherme Carmona, 2016. "Reducible equilibrium properties: comments on recent existence results," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 431-455, March.
    14. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    15. Carmona, Guilherme & Podczeck, Konrad, 2020. "Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games," Journal of Economic Theory, Elsevier, vol. 187(C).
    16. Oriol Carbonell-Nicolau, 2015. "Further results on essential Nash equilibria in normal-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 277-300, June.
    17. Erhan Bayraktar & Alexander Munk, 2016. "High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering," Papers 1605.03653, arXiv.org, revised Mar 2017.
    18. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    19. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2019. "A qualitative theory of large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 497-523, April.
    20. Michael Greinecker & Konrad Podczeck, 2015. "Purification and roulette wheels," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 255-272, February.

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    More about this item

    Keywords

    Existence of equilibrium; measure space of players; discontinuities;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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