Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

By Bar Light, Gabriel Weintraub
October 8,2018Working Paper No. 3731

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.

Keywords
Dynamic games; Mean field equilibrium; Uniqueness of equilibrium; Comparative statics; Dynamic oligopoly models; Heterogeneous agent macroeconomic models