Terminal Ranking Games

Forthcoming, Mathematics of Operations Research

22 Pages Posted: 27 Jun 2019 Last revised: 22 Jun 2020

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: June 23, 2019

Abstract

We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrodinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players' welfare as well as calculate the price of anarchy.

Keywords: tournaments, rank-based rewards, mechanism design, mean field games, price of anarchy, Schrodinger bridges, Lorenz order

Suggested Citation

Bayraktar, Erhan and Zhang, Yuchong, Terminal Ranking Games (June 23, 2019). Forthcoming, Mathematics of Operations Research, Available at SSRN: https://ssrn.com/abstract=3409540 or http://dx.doi.org/10.2139/ssrn.3409540

Erhan Bayraktar

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 (Contact Author)

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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