A note on Poisson contests

We apply the environmental equivalence property of Poisson games (Myerson, In Int J Game Theory 27:375–392, 1998b) to show that, in contests in which the number of contestants is a Poisson random variable with at least two expected contestants and a non-increasing return to effort, ex-ante aggregate effort is less than in a corresponding contest wherein the number of participants is equal to the expected number of contestants under uncertainty. Uncertainty about the number of participants in a rent-seeking contest seems natural. With rent-seeking contests attracting socially wasteful investments of effort or scarce resources, uncertainty generates a social benefit.