The Uniqueness of a Mean Field Equilibrium The lack of a unique equilibrium has significantly limited game theory models' predictive power and their ability to derive robust comparative statics results. Mean field equilibrium has received significant attention in the last decade as a solution concept for dynamic stochastic games because of its computational tractability and behavioral appeal resulting from the reduced assumptions on players' rationality. In "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Light and Weintraub provide conditions that ensure that a mean field equilibrium is unique and derive general comparative statics results in the context of discrete-time mean field games. The paper's existence, uniqueness, and comparative statics results are applied to various models from the economics and operations research literature, including quality ladder models, capacity competition models, advertising competition models, dynamic reputation models, and heterogeneous agent macroeconomic models. 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.
