Teamwise Mean Field Competitions

31 Pages Posted: 22 Jul 2020

See all articles by Xiang Yu

Xiang Yu

Hong Kong Polytechnic University

Yuchong Zhang

University of Toronto - Department of Statistics

Zhou Zhou

The University of Sydney

Date Written: June 24, 2020


This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of team-wise competition game, three optimization problems are introduced when the team size is determined by:

(i) the team manager;

(ii) the central planner;

(iii) the team members’ voting as partnership.

We propose a relative performance criteria for each team member to share the team’s reward and formulate some mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

Suggested Citation

Yu, Xiang and Zhang, Yuchong and Zhou, Zhou, Teamwise Mean Field Competitions (June 24, 2020). Available at SSRN: or

Xiang Yu

Hong Kong Polytechnic University ( email )

11 Yuk Choi Rd
Hung Hom
Hong Kong

Yuchong Zhang

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5

Zhou Zhou (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006

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