Performance responses to competition across sill-levels in rank order tournaments

Tournaments are widely used in the economy to organize production and innovation. We study individual contestant-level data on 2796 contestants in 774 software algorithm design contests with random assignment. Precisely conforming to theory predictions, the performance response to added contestants varies non-monotonically across contestants of different abilities; most respond negatively to competition; highest-skilled contestants respond positively. In counterfactual simulations, we interpret a number of tournament design policies (number of competitors, prize allocation and structure, divisionalization, open entry) as a means of reconciling non-monotonic incentive responses to competition, effectively manipulating the number and skills distribution of contestants facing one another.