All-pay auctions with extra prize : 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. We call this policy an extra prize. The contest organiser splits the prize of the competition into a main prize and an extra prize. Extra prizes differ from second prizes, because they are targeted towards disadvantaged (low-ability) agents. We consider a setting with one high-ability and two low-ability contestants and fully characterise equilibrium. Assuming that the contest organiser aims to maximise expected total effort, we show that (i) almost any extra prize is preferable to a standard all-pay auction without extra prize; (ii) the exclusion principle (Baye, Kovenock and de Vries, 1993) can be implemented by a wide range of sufficiently large extra prizes; and (iii) partial exclusion by means of an appropriately chosen extra prize benefits the organiser more than complete exclusion.