We study a contest environment with a large number of players and prizes that accommodates complete and incomplete information, and heterogeneity among players and prizes. We characterize the effort-maximizing prize structure when players may differ in their marginal valuations for prizes and when the valuation may differ from the designer's cost of providing the prizes. We also provide such a characterization when players' cost of effort differs from the designer's benefit from the effort, as in Moldovanu and Sela (2001).
Contest design with a discrete number of agents and prizes has proven difficult, because even for a given set of prizes: (a) In the models which have been solved in the existing literature, equilibria have complicated structure; (b) In some other settings studied in the literature, the authors were able to provide only an algorithm for deriving equilibria; (c) In some relevant settings, there is no existing characterization of equilibria. In addition, contests can have multiple equilibria, so it is not obvious whether optimal means for the best equilibrium, the worst, or something else.
Because, or perhaps despite of these difficulties, Moldovanu and Sela (2001) obtained some interesting but only partial characterization of the optimal prize structure in discrete contests. We avoid these difficulties by studying the limits of equilibria of discrete contests as the number of players and prizes grow large. This analysis is possible due to the methods developed in Olszewski and Siegel (2014). We characterize the optimal prize structure in large (limit) contests. We confirm Moldovanu and Sela's results in our setting, and establish some additional features of the optimal prize structure.