On the connection between symmetric $N$-player games and mean field games

Abstract

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to \infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate Nash equilibria for the corresponding $N$-player games. The opposite direction is of interest, too: When do sequences of Nash equilibria converge to solutions of an associated mean field game? In this direction, rigorous results are mostly available for stationary problems with ergodic costs. Here, we identify limit points of sequences of certain approximate Nash equilibria as solutions to mean field games for problems with It{ô}-type dynamics and costs over a finite time horizon. Limits are studied through weak convergence of associated normalized occupation measures and identified using a probabilistic notion of solution for mean field games.

References in corpus (4)

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• Mean Field Games and Nonlinear Markov Processes

Cited by in corpus (5)

• From the master equation to mean field game limit theory: A central limit theorem
• A Probabilistic approach to classical solutions of the master equation for large population equilibria
• Satisficing Paths and Independent Multi-Agent Reinforcement Learning in Stochastic Games
• Mixed-strategy Nash equilibrium for a discontinuous symmetric $N$-player game
• The Dyson and Coulomb games