Incentives in Contests with Heterogeneous Solvers

Abstract

In a contest in which heterogeneous solvers make effort to develop solutions, existing theories predict different outcomes about how solvers will change their effort levels as more participants compete for a prize. Specifically, one theory prescribes that when solvers are heterogeneous in their initial expertise, every solver will reduce effort with more participants due to a lower probability of winning the contest. In contrast, another theory prescribes that when solvers are heterogeneous in their costs of exerting effort, high-ability solvers raise their effort with more participants, while low-ability solvers reduce their effort; but it does not provide an explanation for such a prescription. Yet, a recent empirical study corroborates the prescription of the second theory. This paper presents a unifying model that encompasses both types of heterogeneity in solvers, and proves that the result prescribed by the second theory holds in the unifying model, suggesting that the first theory needs to be re-evaluated. Thus, we present the correct analysis of the first theory, and identify a second effect of increased competition on solvers' incentives: More solvers in a contest raise the expected best performance among other solvers, and hence solvers have positive incentives to exert higher effort to win the contest. Due to this positive effect that has been neglected in prior literature, we find that a free-entry open contest is more likely to be optimal to a contest organizer than what prior literature asserted.