On the Exclusion Principle in Tullock Contests

In an influential paper, Fang (Public Choice 112: 351–371, 2002) asserts that the exclusion principle discovered by Baye et al. (1993) for all-pay auction does not apply to lottery in the case in which an organizer cares about the aggregate effort. Serena (2017) shows that the exclusion principle still applies to lottery with (sufficiently) homogeneous contestants if the organizer only cares about the effort of the winner. In this paper, we consider a Tullock lottery contest in which contestants' types are binary and stochastic and the two types are significantly different. We find that Fang's (2002) result still holds but Serena's (2017) result does not. Precisely, to increase the expected winner's effort, it is strictly beneficial to exclude all but two contestants if and only if each contestant's probability of being the weak type is small. If the probability is sufficiently high, it is optimal to include all contestants.