Prizes and effort in contests with private information

We consider contests where participants have private information about their ability and the contest designer can manipulate the values of different prizes to influence effort. We study the effect on effort of two different interventions: increase in the value of prizes and increase in competition (transfer of value from worse to better prizes). We identify two natural sufficient conditions on the distribution of abilities in the population under which both interventions have opposite effects on effort. More precisely, we find that if the density of agents is decreasing in ability so that unproductive agents are more likely than productive agents, the two interventions encourage effort. And if this density is monotone increasing in ability, the interventions discourage effort. We discuss applications to the design of optimal contests in three different environments, including the design of grading contests. Assuming the value of a grade is determined by the information it reveals about the agent's ability, we establish a link between the informativeness of a grading scheme and the effort induced by it.