Design tools for all-pay contests: Aligning incentives and balancing the playing field

Abstract

In contests where players compete across multiple dimensions, we compare two main design tools available to a designer with a fixed prize budget: prize allocation, which distributes the budget across independent single-dimensional contests, and the scoring rule, which awards the entire budget to the winner based on weighted overall performance. In an all-pay framework with a multiplicative (designer) payoff, the scoring rule dominates prize allocation through two channels: an incentive-alignment effect, aligning players’ strategies with the designer’s objective, and a balancing effect, which favors the weaker player and raises output. When handicaps are introduced as an additional tool, both players’ equilibrium payoffs are zero, eliminating the balancing effect so that only incentive alignment matters. Finally, with additive (designer) payoffs, outputs are substitutes: the scoring rule continues to outperform under asymmetry but coincides with prize allocation under symmetry.