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A Mean Field Competition

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  • Marcel Nutz
  • Yuchong Zhang

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.

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  • Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.
    • Handle: RePEc:arx:papers:1708.01308
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    References listed on IDEAS

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    Cited by:

    1. Marcel Nutz & Jaime San Martin & Xiaowei Tan, 2018. "Convergence to the Mean Field Game Limit: A Case Study," Papers 1806.00817, arXiv.org, revised May 2019.

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