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Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk

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  • Lukasz Balbus
  • Pawel Dziewulski
  • Kevin Reffett
  • Lukasz Wozny

Abstract

We present a new approach for studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Distributional Equilibrium (MSDE), prove its existence, and provideconstructive methods for characterizing and comparing equilibrium distributional transitional dynamics. To analyze equilibrium transitions for the distributions ofprivate types, we develop an appropriate dynamic (exact) law of large numbers.Finally, we show that our models can be approximated as idealized limits of gameswith a large (but finite) number of players. We provide numerous applications of theresults including: dynamic models of growth with status concerns, social distance and paternalistic bequest with endogenous preference for consumption.

Suggested Citation

  • Lukasz Balbus & Pawel Dziewulski & Kevin Reffett & Lukasz Wozny, 2020. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," KAE Working Papers 2020-052, Warsaw School of Economics, Collegium of Economic Analysis.
    • Handle: RePEc:sgh:kaewps:2020052
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    Cited by:

    1. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    2. 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.
    3. 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.

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    More about this item

    Keywords

    large games; distributional equilibria; supermodular games; compara-tive dynamics; non-aggregative games; law of large numbers; social interactions;
    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
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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