Mean field games with incomplete information

TL;DR

This paper studies mean field games where players lack information about others' distributions, establishing existence, uniqueness, and deriving a master equation under different informational scenarios.

Contribution

It introduces a novel analysis of mean field games with incomplete information, including existence, uniqueness, and the derivation of a master equation.

Findings

Existence and uniqueness of solutions in the uninformed case

Derivation of a master equation when players observe payments

Partial results on solution uniqueness in the informed case

Abstract

This paper is concerned with mean field games in which the players do not know the repartition of the other players. First a case in which the players do not gain information is studied. Results of existence and uniqueness are proved and discussed. Then, a case in which the players observe the payments is investigated. A master equation is derived and partial results of uniqueness are given for this more involved case.