Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

56 Pages Posted: 13 Nov 2018 Last revised: 31 Oct 2019

See all articles by Bar Light

Bar Light

Stanford University, Graduate School of Business

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University

Date Written: October 8, 2018

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 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.

Suggested Citation

Light, Bar and Weintraub, Gabriel Y., Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics (October 8, 2018). Columbia Business School Research Paper No. 19-1; Stanford University Graduate School of Business Research Paper No. 19-3. Available at SSRN: https://ssrn.com/abstract=3265048 or http://dx.doi.org/10.2139/ssrn.3265048

Bar Light

Stanford University, Graduate School of Business ( email )

Stanford, CA
United States

Gabriel Y. Weintraub (Contact Author)

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

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