A rank based mean field game in the strong formulation

Abstract

We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite player game and obtain the rate of convergence.

arXiv commentFinal version. To appear in Electronic Communications in Probability. Keywords: Mean Field Games, competition/tournaments, common noise, rank dependent interaction, non-local interaction, strong formulation