A Mean Field Competition

TL;DR

This paper introduces a mean field game model with rank-based rewards, analyzing optimal effort and reward scheme design to minimize the time for a fraction of agents to reach a goal.

Contribution

It presents a tractable Poissonian model for rank-based mean field games and explicitly solves the principal--agent problem for optimal reward design.

Findings

Optimal effort strategies derived for given reward schemes

Explicit reward scheme minimizes time to reach target fraction

Model provides insights into competitive effort dynamics

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.