DP16504 Subsidy and Taxation in All-Pay Auctions under Incomplete Information

Author(s): Yizhaq Minchuk, Aner Sela
Publication Date: September 2021
Date Revised: September 2021
Keyword(s): all-pay auctions, Subsidy, taxation
JEL(s): C72, D44, H25
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=16504

We study all-pay auctions under incomplete information with n contestants who have non-linear cost functions. The designer may award two kinds of subsidy (taxation): one that decreases (increases) each contestant's marginal cost of effort and another that increases (decreases) each contestant's value of winning. The designer's expected payoff is the contestants' expected total effort minus the cost of subsidy or, alternatively, plus the tax payment. We show that when the resource of subsidy (the marginal taxation rate) is relatively small and the cost function is concave (convex), the designer's expected payoff in all-pay auctions with both kinds of subsidy (taxation) is higher than in the same contest without any subsidy (taxation). We then compare both kinds of subsidy and demonstrate that if the resource of subsidy is relatively small and the cost functions are concave (convex), the cost subsidy is better than prize subsidy for the designer who wishes to maximize his expected payoff.