Optimal grading contests

We study the design of grading contests between agents with private information about their abilities under the assumption that the value of a grade is determined by the information it reveals about the agent's productivity. Towards the goal of identifying the effort-maximizing grading contest, we study the effect of increasing prizes and increasing competition on effort and find that the effects depend qualitatively on the distribution of abilities in the population. Consequently, while the optimal grading contest always uniquely identifies the best performing agent, it may want to pool or separate the remaining agents depending upon the distribution. We identify sufficient conditions under which a rank-revealing grading contest, a leaderboard-with-cutoff type grading contest, and a coarse grading contest with at most three grades are optimal. In the process, we also identify distributions under which there is a monotonic relationship between the informativeness of a grading scheme and the effort induced by it.