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

Matthias Dahm

Recently, the rules for participation of the Man Booker Prize for Fiction were changed. Initially, only novelists from the UK, Commonwealth, Ireland and Zimbabwe were eligible to receive the prize. With the new rules, all fiction in English published worldwide is eligible. This, of course, increases competition. There is however concern that, because of the rule change, new novelists will lose against established writers and find it more difficult to win recognition. In this sense, one can think of the prize with the initial restricted participation rule as an affirmative action policy: The Booker prize is a targeted prize for some competitors, in addition to the main competition in which all novelists compete for recognition. This raises the question what the incentive effects of such a policy are.

In this Nottingham School of Economics working paper, published in the International Journal of Industrial Organization, Matthias Dahm investigates this question using an all-pay auction, which is a well-established tool for modeling competition. What distinguishes the example above from the standard contest model of competition is that players that belong to a disadvantaged group compete for a prize that others do not have access to. This creates a very specific prize structure. All agents compete for the main prize, but only disadvantaged players contest the extra prize. The main result of this paper is that such an extra prize enhances competition. Consequently, even a contest designer who is not interested in affirmative action per se might decide to establish it. More precisely, the paper considers a setting with one high-ability and two low-ability contestants and fully characterise equilibrium. Under the assumption that the contest organiser aims to maximise expected total effort, it is shown 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.

International Journal of Industrial Organization, "Semi-targeted all-pay auctions: a partial exclusion principle", by Matthias Dahm. https://doi.org/10.1016/j.ijindorg.2018.09.003

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