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http://hdl.handle.net/10397/93843
Title: | Teamwise mean field competitions | Authors: | Yu, X Zhang, Y Zhou, Z |
Issue Date: | Dec-2021 | Source: | Applied mathematics and optimization, Dec. 2021, v. 84, suppl. 1, p. S903-S942 | Abstract: | 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. | Keywords: | Equilibrium team size Mean field game of mean field games Optimal team size Rank-based reward Teamwork formulation |
Publisher: | Springer | Journal: | Applied mathematics and optimization | ISSN: | 0095-4616 | EISSN: | 1432-0606 | DOI: | 10.1007/s00245-021-09789-1 | Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00245-021-09789-1 |
Appears in Collections: | Journal/Magazine Article |
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Yu_Teamwise_Mean_Field.pdf | Pre-Published version | 1.94 MB | Adobe PDF | View/Open |
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