Learning in Mean Field Games: the Fictitious Play

TL;DR

This paper introduces a fictitious play-based learning procedure for mean field games and proves its convergence in potential cases, advancing understanding of equilibrium computation in large-scale differential games.

Contribution

It presents a novel learning algorithm for mean field games and establishes its convergence in potential scenarios, bridging game theory and learning dynamics.

Findings

Convergence of the proposed learning procedure in potential mean field games.

Extension of fictitious play concepts to infinite-agent differential games.

Theoretical validation of learning dynamics in mean field game settings.

Abstract

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its convergence when the Mean Field Game is potential.