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Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

Author

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  • Light, Bar

    (Graduate School of Business, Stanford University)

  • Weintraub, Gabriel

    (Graduate School of Business, Stanford University)

Abstract

The standard solution concept for stochastic games is Markov perfect equilibrium (MPE); however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE) that has been popularized in the recent literature. MFE takes advantage of averaging effects in models with a large number of agents. We make three main contributions. First, our main result in the paper provides conditions that ensure the uniqueness of an MFE. Second, we generalize previous MFE existence results. Third, we provide general comparative statics results. We apply our results to dynamic oligopoly models and to heterogeneous agent macroeconomic models commonly used in previous work. We believe our uniqueness result is the first of its nature in the class of models we study.

Suggested Citation

  • Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3731
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    Cited by:

    1. Bar Light, 2019. "General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond," Papers 1906.06810, arXiv.org, revised Mar 2021.
    2. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    3. Daron Acemoglu & Martin Kaae Jensen, 2018. "Equilibrium Analysis in the Behavioral Neoclassical Growth Model," NBER Working Papers 25363, National Bureau of Economic Research, Inc.
    4. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    5. Bar Light, 2020. "Uniqueness of equilibrium in a Bewley–Aiyagari model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 435-450, March.

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