Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 2019 | Submitted
Journal Article Open

Large tournament games

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.

Additional Information

© 2019 Institute of Mathematical Statistics. Erhan Bayraktar is supported in part by the NSF under grant DMS-1613170 and by the Susan M. Smith Professorship. Jakša Cvitanić is supported in part by the NSF under grant DMS-DMS-1810807. Yuchong Zhang was supported by the NSF under grant DMS-1714607. We are grateful to Marcel Nutz for many stimulating discussions.

Attached Files

Submitted - 1811.00076.pdf

Files

1811.00076.pdf
Files (1.9 MB)
Name Size Download all
md5:c7680bdf2ada41d23ca28144be97704e
1.9 MB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 19, 2023