Prizes and effort in contests with private information

Contests are situations in which agents compete with one another by exerting costly effort to win valuable prizes. In this paper, we consider contest environments where participants have private information about their ability and the contest designer can manipulate the values of different prizes to influence the effort exerted by them. In such environments, with the goal of understanding how different contests compare in terms of the effort they induce, we study the effect of two different interventions on effort:

(1) increase in value of prizes

(2) increase in competition (transfer of value from worse to better prizes)

The effect of increasing the value of a prize on effort depends upon the rank of the prize. While increasing the value of the first prize encourages effort for all agent types and increasing the value of the last prize discourages effort for all agent types, the effect of increasing the value of any intermediate prize depends qualitatively on the distribution of abilities in the population. More precisely, we find that if the density of agents is increasing in ability so that productive agents are more likely than unproductive agents, increasing any intermediate prize discourages effort. And if the density of agents is decreasing in ability so that unproductive agents are more likely than productive agents, increasing any intermediate prize encourages effort. Intuitively, this is because increasing any intermediate prize reduces effort of the most productive agents while increasing the effort of the less productive agents. The overall expected effect then depends on the relative likelihood of the more productive and less productive agents.