Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

Bar Light () and Gabriel Y. Weintraub ()
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Bar Light: Graduate School of Business, Stanford University, Stanford, California 94305
Gabriel Y. Weintraub: Graduate School of Business, Stanford University, Stanford, California 94305

Operations Research, 2022, vol. 70, issue 1, 585-605

Abstract: The standard solution concept for stochastic games is Markov perfect equilibrium; however, its computation becomes intractable as the number of players increases. Instead, we consider mean field equilibrium (MFE), which has been popularized in recent literature. MFE takes advantage of averaging effects in models with a large number of players. We make three main contributions. First, our main result provides conditions that ensure the uniqueness of an MFE. We believe this uniqueness result is the first of its nature in the class of models we study. 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 in economics and operations.

Keywords: Stochastic Model Applications; dynamic games; mean field equilibrium; uniqueness of equilibrium; comparative statics; dynamic oligopoly models; heterogeneous agent macroeconomic models (search for similar items in EconPapers)
Date: 2022
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