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 designer's payoff under the optimal lottery is equal to his expected payoff under the optimal all-pay auction.