From monopoly to competition: When do optimal contests prevail?

We study competition among multiple contest designers in a general model. The goal of each contest designer is to maximize the sum of efforts of the contestants participating in their contest. Assuming symmetric contestants, our main result shows that the optimal contests in the monopolistic setting (i.e., those that maximize the sum of efforts in a model with a single contest designer) form an equilibrium in the model with competition. Under a very natural assumption, these contests are dominant, and the equilibrium that they form is unique. Moreover, the equilibria with the optimal contests are Pareto-optimal even when other equilibria emerge. In many natural cases, they also maximize the social welfare. Additional examples show that, with further generalizations of our model, optimal contests no longer prevail. Our results therefore highlight and clarify the borderline between settings in which optimal contests prevail and do not prevail.