Optimal Reward and Mean Field Game of Racing Yuchong Zhang Columbia University We formulate a tractable mean field game of exit time control, where players compete to finish a given project, and are rewarded based on the ranking of their completion times. Such a model features relative performance evaluation, an important topic in contract theory. Our goal here is to understand the equilibrium behavior and design a rank-based reward scheme that encourages early completion, given that the planner has a limited budget, or to minimize the budget given a desired rate of completion. In a one-stage Poisson race, closed-form solution to the central planner's problems can be found by solving a constrained calculus of variation problem, and the solution appear to be time-inconsistent.