Teamwise Mean Field Competitions

Xiang Yu, Yuchong Zhang, Zhou Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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 teamwise 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 special cases of 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.

Original languageEnglish
Pages (from-to)903-942
Number of pages40
JournalApplied Mathematics and Optimization
Issue number1
Early online date29 May 2021
Publication statusPublished - Dec 2021


  • Equilibrium team size
  • Mean field game of mean field games
  • Optimal team size
  • Rank-based reward
  • Teamwork formulation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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