Terminal Ranking Games

被引：5
作者：
Bayraktar, Erhan [1 ]
Zhang, Yuchong [2 ]
机构：
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48104 USA
[2] Univ Toronto, Dept Stat Sci, Toronto, ON M5G 1Z5, Canada
来源：
MATHEMATICS OF OPERATIONS RESEARCH | 2021年 / 46卷 / 04期
基金：
美国国家科学基金会;
关键词：
tournaments; rank-based rewards; mechanism design; mean field games; price of anarchy; Schrodinger bridges; Lorenz order; MEAN-FIELD GAMES;
D O I：
10.1287/moor.2020.1107
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrodinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players' welfare as well as calculate the price of anarchy.
引用
收藏
页码：1349 / 1365
页数：18
相关论文
共 21 条
[1]   LARGE TOURNAMENT GAMES [J].
Bayraktar, Erhan ;
Cvitanic, Jaksa ;
Zhang, Yuchong .
ANNALS OF APPLIED PROBABILITY, 2019, 29 (06) :3695-3744
[2]   A rank-based mean field game in the strong formulation [J].
Bayraktar, Erhan ;
Zhang, Yuchong .
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2016, 21
[3]   ON THE (IN)EFFICIENCY OF MFG EQUILIBRIA [J].
Cardaliaguet, Pierre ;
Rainer, Catherine .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2019, 57 (04) :2292-2314
[4]  
Carmona Rene, 2019, ESAIM: Proceedings and Surveys, V65, P349, DOI 10.1051/proc/201965349
[5]  
Carmona R, 2018, PROB THEOR STOCH MOD, V84, P1, DOI 10.1007/978-3-319-56436-4
[6]   A PROBABILISTIC WEAK FORMULATION OF MEAN FIELD GAMES AND APPLICATIONS [J].
Carmona, Rene ;
Lacker, Daniel .
ANNALS OF APPLIED PROBABILITY, 2015, 25 (03) :1189-1231
[7]   On the Relation Between Optimal Transport and Schrodinger Bridges: A Stochastic Control Viewpoint [J].
Chen, Yongxin ;
Georgiou, Tryphon T. ;
Pavon, Michele .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 169 (02) :671-691
[8]  
F H., 1988, COLE D T PROBABILIT, V1362, P101, DOI 10.1007/BFb0086180
[9]  
Fang DW, 2020, J POLIT ECON, V128, P1940
[10]   Mean Field Games and Applications [J].
Gueant, Oliviier ;
Lasry, Jean-Michel ;
Lions, Pierre-Louis .
PARIS-PRINCETON LECTURES ON MATHEMATICAL FINANCE 2010, 2011, 2003 :205-266
123