Carrots and Sticks: Collaboration of Taxation and Subsidies in Contests

We study all-pay auctions under incomplete information in which the designer can impose taxes or subsidies, and his expected payoff is the contestants' expected total effort minus the cost of subsidies, or, alternatively, plus the tax payment. When contestants have linear effort cost functions, we show that taxing the winner's payoff is profitable for the contest designer, and particularly more profitable than the same model with no taxation or the same model with contestants' effort taxation. When the contestants' effort cost functions are convex and the taxation rate is relatively low, we show that the designer should tax the winner's payoff while subsidizing all of the other contestants' effort costs. As a result, contest organizers should think about combining taxation and subsidies in their contests because they complement rather than substitute each other.