Correlated equilibria for mean field games with progressive strategies

TL;DR

This paper introduces a new framework for analyzing mean field games using correlated equilibria, providing a robust approximation method for large symmetric games with explicit examples.

Contribution

It defines correlated solutions in mean field games, enabling the construction of approximate N-player correlated equilibria with robustness to progressive deviations.

Findings

Defined correlated solutions for mean field games

Constructed approximate N-player correlated equilibria

Provided explicit example solutions

Abstract

In a discrete space and time framework, we study the mean field game limit for a class of symmetric $N$-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows to construct approximate $N$-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.