On the Optimal Design of Lottery Contests

Abstract

This paper develops a novel technique that allows us to characterize the optimal biased generalized lottery contest. In our baseline setting, we search for the optimal multiplicative biases for asymmetric Tullock contests — i.e., the weights placed on contestants' effort entries in the contest success function. Asymmetric Tullock contests, in general, have no closed-form solutions, which nullifies the usual implicit programming approach. We propose an alternative approach that allows us to circumvent this difficulty and characterize the optimum toward a wide array of objectives without solving for the equilibrium explicitly. The results of optimization exercises yield novel implications on the strategic nature of the contest game and its optimal design. In particular, we show that the conventional wisdom of leveling the playing field does not generally hold. Further, we relax restrictions on the functional forms, allow for enriched design space, and address more general objective functions. We show that our approach applies flexibly in a wide array of contexts and generates broad implications.