# Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics

## TL;DR

This paper establishes conditions for the uniqueness, existence, and comparative statics of mean field equilibrium in large-player stochastic games, facilitating analysis where traditional methods are computationally infeasible.

## Contribution

It provides the first known uniqueness conditions for MFE, generalizes existence results, and offers broad comparative statics applicable to economic and operational models.

## Key findings

- Proved conditions ensuring MFE uniqueness.
- Generalized MFE existence results.
- Derived comparative statics for large-player models.

## 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.