Semi-targeted all-pay auctions: A partial exclusion principle

This paper studies the effects of a specific affirmative action policy in complete information all-pay auctions when players differ in ability. The contest organizer splits the overall prize of the competition into a targeted and an untargeted prize. The targeted prize is exclusively for disadvantaged (low-ability) agents and excludes advantaged agents partially from the overall prize. We consider a setting with one high-ability and two low-ability contestants and fully characterize equilibrium. Assuming that the contest organizer aims to maximize expected total effort, we show that (i) almost any targeted prize is preferable to a standard all-pay auction without targeted prize; (ii) the exclusion principle Baye et al. (1993) can be implemented by a wide range of sufficiently large targeted prizes; and (iii) partial exclusion by means of an appropriately chosen targeted prize benefits the organizer more than complete exclusion. We also discuss the robustness of our results in settings with more than three agents.