Lotteries vs. All-Pay Auctions in Fair and Biased Contests

The form of contests for a single fixed prize can be determined by a designer who maximizes the contestants' efforts. This paper establishes that, under common knowledge of the two asymmetric contestants' prize valuations, a fair Tullock-type endogenously determined lottery is always superior to an all-pay-auction; it yields larger expected efforts (revenues) for the contest designer. If the contest can be unfair (structural discrimination is allowed), then the optimal lottery cannot be dominated by an all-pay-auction.

Keywords: contest design, efforts (revenue) maximization, discrimination, endogenous lottery, all-pay auction.

JEL Classification: D70, D71,D72