Equivalence of optimal noisy-ranking contests and Tullock contests

We analyze a noisy-ranking contest in which participants compete in several dimensions. The organizer randomly samples a number of dimensions and awards a prize to the most productive agent. When the contest is optimally designed, we establish a structural equivalence between this family of noisy-ranking contests and contests built upon Tullock contest success functions. Our result also shows that in this class of noisy-contests, the profit-maximization problem of the planner can be turned into a stochastic choice problem for a planner who has some deterministic preferences over the contestants' win probabilities.