LARGE TOURNAMENT GAMES

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Cvitanic, Jaksa; Zhang, Yuchong
• 署名单位: University of Michigan System; University of Michigan; California Institute of Technology; University of Toronto
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1490
• 发表日期: 2019
• 页码: 3695-3744
• 关键词: mean-field games; systems

摘要

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.