Large Tournament Games

57 Pages Posted: 12 Feb 2018 Last revised: 5 Nov 2018

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Jaksa Cvitanic

California Institute of Technology - Division of the Humanities and Social Sciences

Yuchong Zhang

University of Toronto

Date Written: February 6, 2018

Abstract

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank dependent, the equilibrium has a surprisingly explicit characterization, which allows us to conduct comparative statics and obtain explicit solution to several optimal reward design problems. In the general case when the players are heterogenous and payoffs are not purely rank dependent, we prove the existence, uniqueness and stability of the Nash equilibrium of the associated mean field game, and the existence of an approximate Nash equilibrium of the finite-player game. Our results have some potential economic implications; e.g., they lend support to government subsidies for R&D, assuming the profits to be made are substantial.

Keywords: Tournaments, rank-based rewards, mechanism design, mean field games, bifurcation diagram of Nash equilibria

Suggested Citation

Bayraktar, Erhan and Cvitanic, Jaksa and Zhang, Yuchong, Large Tournament Games (February 6, 2018). Available at SSRN: https://ssrn.com/abstract=3119212 or http://dx.doi.org/10.2139/ssrn.3119212

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

Jaksa Cvitanic (Contact Author)

California Institute of Technology - Division of the Humanities and Social Sciences ( email )

1200 East California Blvd.
Pasadena, CA 91125
United States

HOME PAGE: http://www.hss.caltech.edu/~cvitanic/

Yuchong Zhang

University of Toronto ( email )

Toronto, Ontario M5S 3G8
Canada

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