Nonparametric Identification and Estimation of Contests with Uncertainty

Real-world contests are inherently uncertain since the player who exerts the highest effort can still lose. In this paper, I consider a general asymmetric incomplete information contest model with a nonparametric distribution of uncertainty in the contest success function. It generalizes all-pay auctions, Tullock contests, and rank-order tournaments with two asymmetric players. Uncertainty in the contest success function summarizes other factors that influence the contest win outcome apart from the efforts of the players, such as, for example, players’ reputation or luck. First, I nonparametrically identify and estimate the distribution of uncertainty using the information on contest win outcomes and efforts. Next, I nonparametrically identify and estimate the distributions of the players’ costs of exerting effort. The model provides a method to disentangle two sources of player’s advantage: asymmetry in the costs’ distributions and the effect of the uncertainty distribution on the winning probability. As an empirical example, I apply the model to the U.S. House of Representatives elections.