A Mean Field Competition

33 Pages Posted: 4 Aug 2017

See all articles by Marcel Nutz

Marcel Nutz

Columbia University

Yuchong Zhang

University of Toronto - Department of Statistics

Date Written: August 3, 2017

Abstract

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable Poissonian model in which we can describe the optimal effort for a given reward scheme. Second, we study the principal--agent problem of designing an optimal reward scheme. A surprising, explicit design is found to minimize the time until a given fraction of the population has reached the goal.

Keywords: Mean Field Game, Rank-Based Reward, Optimal Contract, R and D Competition

Suggested Citation

Nutz, Marcel and Zhang, Yuchong, A Mean Field Competition (August 3, 2017). Available at SSRN: https://ssrn.com/abstract=3013429 or http://dx.doi.org/10.2139/ssrn.3013429

Marcel Nutz

Columbia University ( email )

Yuchong Zhang (Contact Author)

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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