On the Optimality of Small Research Tournaments

Abstract

I study two open questions concerning optimal tournament size in Fullerton and McAfee's (1999) model of research tournaments with heterogeneous contestants. For the case where firms' costs are commonly known prior to the tournament and the procurer can charge non-discriminatory entry fees, I prove a sharp, worst-case bound for the ratio between the cost of procuring a given total effort from the optimal number of contestants and the corresponding cost for a tournament of size two. The analysis confirms the attractiveness of the smallest possible tournament, with some notable exceptions. I then describe the problem of inducing a given expected total effort at the lowest expected cost, by choosing the optimal combination of prize and tournament size, when firms are privately informed about their i.i.d. marginal costs prior to the tournament and a set of lowest-cost contestants is selected by an entry auction. I show that this problem can be solved in closed form when marginal costs are uniformly distributed on [0,c], and that the result for this case strongly favors the smallest possible tournament.