Mean-Field Games Under Model Uncertainty

TL;DR

This paper investigates mean-field games under model uncertainty, analyzing how ambiguity in transition probabilities affects equilibrium strategies and establishing the connection between finite-agent games and their mean-field limits.

Contribution

It introduces a framework for MFGs with model uncertainty, proving existence of equilibria, asymptotic relations with finite games, and providing a solvable example with explicit solutions.

Findings

MFG equilibria form approximate Nash equilibria in large populations

Limits of finite-agent equilibria are MFG equilibria

Existence of equilibria proven for finite-agent and mean-field models

Abstract

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within an uncertainty set. Unlike in classical MFGs, model uncertainty renders the population distribution flow stochastic. This leads us to consider strategies that depend on both individual states and the realized distribution of the population. Our main results establish the asymptotic relationship between $N$-agent games and MFGs: every MFG equilibrium constitutes an $\varepsilon$-Nash equilibrium for sufficiently large populations, and conversely, limits of $N$-agent equilibria are MFG equilibria. We also prove the existence of equilibria for finite-agent games and construct a solvable mean-field example with closed-form solutions.