Lottery versus all-pay auction contests: A revenue dominance theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).