Contests Where There is Variation in the Marginal Productivity of Effort

We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function and that output is increasing in ability. We also show that marginal effort is increasing in ability and that effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win; however, abilities are now assumed to be independently distributed. We analyze the contest designer's decisions in choosing contest rules optimal from her point of view. We characterize the solution in terms of continuity and exclusion of low ability participants. We also show that under the conditions imposed, the output produced and probability of winning are increasing in ability (whenever this probability is between zero and one). We also examine when the equilibrium probability of winning can be zero or one, and the relationship between the marginal cost of producing output and the marginal utility per dollar of the net award for winning. Finally, we show that the contest designer's expected revenue is increasing in the ability of contestants