Some remarks on Mean Field Games

TL;DR

This paper explores three key aspects of Mean Field Games, including strategy-dependent dynamics, noise modeling in discrete spaces, and the reduction to agent-based models as players' anticipation diminishes.

Contribution

It provides new insights into strategy interactions, noise formulation, and the limiting behavior of Mean Field Games, extending their theoretical framework.

Findings

Strategy-dependent dynamics analyzed

Master Equation for discrete noise modeled

Reduction to agent-based models shown

Abstract

We study in this paper three aspects of Mean Field Games. The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one concerns the modeling of '' noise '' in discrete space models and the formulation of the Master Equation in this case. Finally, we show how Mean Field Games reduce to agent based models when the intertemporal preference rate goes to infinity, i.e. when the anticipation of the players vanishes.