Stable solutions in potential mean field game systems

TL;DR

This paper introduces the concept of stable solutions in potential mean field game systems, showing they are locally isolated and serve as attractors for learning algorithms, advancing understanding of solution stability.

Contribution

It defines stable solutions in mean field games, proves their existence in potential cases, and demonstrates their role as local attractors for learning processes.

Findings

Stable solutions are locally isolated in potential mean field games.

Such solutions exist and can be characterized mathematically.

They act as local attractors for learning algorithms.

Abstract

We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning procedures.