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Large tournament games

Bayraktar, Erhan and Cvitanić, Jakša and Zhang, Yuchong (2019) Large tournament games. Annals of Applied Probability, 29 (6). pp. 3695-3744. ISSN 1050-5164. doi:10.1214/19-aap1490. https://resolver.caltech.edu/CaltechAUTHORS:20200123-081310030

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1214/19-aap1490DOIArticle
https://arxiv.org/abs/1811.00076arXivDiscussion Paper
ORCID:
AuthorORCID
Cvitanić, Jakša0000-0001-6651-3552
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1613170
Susan M. Smith ProfessorshipUNSPECIFIED
NSFDMS-1810807
NSFDMS-1714607
Subject Keywords:Tournaments; rank-based rewards; mechanism design; mean field games
Issue or Number:6
Classification Code:MSC: Primary: 91A13: Games with infinitely many players. Secondary: 91B40: Labor market, contracts 93E20: Optimal stochastic control
DOI:10.1214/19-aap1490
Record Number:CaltechAUTHORS:20200123-081310030
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200123-081310030
Official Citation:Bayraktar, Erhan; Cvitanić, Jakša; Zhang, Yuchong. Large tournament games. Ann. Appl. Probab. 29 (2019), no. 6, 3695--3744. doi:10.1214/19-AAP1490. https://projecteuclid.org/euclid.aoap/1578366324
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100864
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Jan 2020 17:07
Last Modified:16 Nov 2021 17:57

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