A Mean Field Competition

Marcel Nutz; Yuchong Zhang

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arXiv · 1708.01308

A Mean Field Competition

Marcel Nutz·Yuchong Zhang

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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. 2017-08-03. A Mean Field Competition. https://arxiv.org/abs/1708.01308

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