Large Tournament Games

56 Pages Posted: 12 Feb 2018  

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 tournament game in which each player is rewarded based on her rank in terms of the time of reaching a goal. We prove existence, uniqueness and stability of the game with infinitely many players, existence of an approximate equilibrium with finitely many players, and find an explicit characterization when players are homogeneous. In our setup we find that:

(i) the welfare may be increasing in cost of effort; (ii) when the total pie is small, the aggregate effort may be increasing in prize inequality, unlike in Fang, Noe and Strack (2018); (iii) the welfare may go up with a higher percentage of unskilled workers, as do the completion rates of the skilled and unskilled sub-populations.

Our results 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

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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