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December 2019 Large tournament games
Erhan Bayraktar, Jakša Cvitanić, Yuchong Zhang
Ann. Appl. Probab. 29(6): 3695-3744 (December 2019). DOI: 10.1214/19-AAP1490

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.

Citation

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Erhan Bayraktar. Jakša Cvitanić. Yuchong Zhang. "Large tournament games." Ann. Appl. Probab. 29 (6) 3695 - 3744, December 2019. https://doi.org/10.1214/19-AAP1490

Information

Received: 1 October 2018; Revised: 1 March 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172344
MathSciNet: MR4047990
Digital Object Identifier: 10.1214/19-AAP1490

Subjects:
Primary: 91A13
Secondary: 91B40, 93E20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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