Bayesian Learning in Mean Field Games

TL;DR

A mean field system satisfied by the equilibrium payoff of the game is derived and the existence of a solution under standard regularity assumptions is proved.

Abstract

We consider a mean-field game model where the cost functions depend on a fixed parameter, called \textit{state}, which is unknown to players. Players learn about the state from a a stream of private signals they receive throughout the game. We derive a mean field system satisfied by the equilibrium payoff of the game and prove existence of a solution under standard regularity assumptions. Additionally, we establish the uniqueness of the solution when the cost function satisfies the monotonicity assumption of Lasry and Lions at each state.

Theorems & Definitions (10)

• Lemma 2.1
• proof
• Lemma 2.2
• proof
• Definition 2.3
• Remark 2.4
• Theorem 3.1
• proof
• Theorem 4.1
• proof