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A qualitative theory of large games with strategic complementarities

Author

Listed:
  • Łukasz Balbus

    (University of Zielona Góra)

  • Paweł Dziewulski

    (University of Oxford)

  • Kevin Reffett

    (Arizona State University)

  • Łukasz Woźny

    (Warsaw School of Economics)

Abstract

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators defined on the space of distributions partially ordered with respect to the first-order stochastic dominance, we prove existence of a greatest and least distributional Nash equilibrium. In particular, we obtain our results under a different set of conditions than those in the existing literature. Moreover, we provide computable monotone distributional equilibrium comparative statics with respect to the parameters of the game. Finally, we apply our results to models of social distance, large stopping games, keeping up with the Joneses, as well as a general class of linear non-atomic games.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:67:y:2019:i:3:d:10.1007_s00199-017-1075-7
    DOI: 10.1007/s00199-017-1075-7
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    References listed on IDEAS

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    Cited by:

    1. Rabah Amir, 2020. "Special Issue: Supermodularity and Monotonicity in Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 907-911, November.
    2. Takashi Kamihigashi & Kevin Reffett & Masayuki Yao, 2014. "An Application of Kleene's Fixed Point Theorem to Dynamic Programming: A Note," Working Papers 2014-398, Department of Research, Ipag Business School.
    3. Adriana Gama & Rim Lahmandi-Ayed & Ana Elisa Pereira, 2020. "Entry and mergers in oligopoly with firm-specific network effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1139-1164, November.
    4. Łukasz Balbus & Paweł Dziewulski & Kevin Reffett & Łukasz Woźny, 2015. "Differential information in large games with strategic complementarities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 201-243, May.
    5. Rabah Amir, 2018. "Special issue: supermodularity and monotone methods in economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 547-556, October.
    6. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    7. Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.
    8. Rene Carmona & Francois Delarue & Daniel Lacker, 2016. "Mean field games of timing and models for bank runs," Papers 1606.03709, arXiv.org, revised Jan 2017.
    9. Pavlo Prokopovych & Nicholas C. Yannelis, 2022. "On nondegenerate equilibria of double auctions with several buyers and a price floor," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 625-654, April.
    10. Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.
    11. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    Large games; Distributional equilibria; Supermodular games; Games with strategic complementarities; Computation of equilibria; Non-aggregative games;
    All these keywords.

    JEL classification:

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

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