A Rank-Based Mean Field Game in the Strong Formulation

Electronic Communications in Probability, 21, paper no. 72, 1-12, 2016

12 Pages Posted: 13 May 2016 Last revised: 30 Jun 2019

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yuchong Zhang

University of Toronto - Department of Statistics

Date Written: March 21, 2016

Abstract

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

Keywords: Mean Field Games, Competition, Common Noise, Rank-Dependent Interaction, Non-Local Interaction, Strong Formulation

Suggested Citation

Bayraktar, Erhan and Zhang, Yuchong, A Rank-Based Mean Field Game in the Strong Formulation (March 21, 2016). Electronic Communications in Probability, 21, paper no. 72, 1-12, 2016, Available at SSRN: https://ssrn.com/abstract=2779255 or http://dx.doi.org/10.2139/ssrn.2779255

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yuchong Zhang

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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