A rank based mean field game in the strong formulation
Probability
2016-10-18 v3 Optimization and Control
Mathematical Finance
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.
Cite
@article{arxiv.1603.06312,
title = {A rank based mean field game in the strong formulation},
author = {Erhan Bayraktar and Yuchong Zhang},
journal= {arXiv preprint arXiv:1603.06312},
year = {2016}
}
Comments
Final version. To appear in Electronic Communications in Probability. Keywords: Mean Field Games, competition/tournaments, common noise, rank dependent interaction, non-local interaction, strong formulation