Asymmetric All-Pay Contests with Heterogeneous

This paper studies complete-information, all-pay contests with asymmetric players competing for multiple heterogeneous prizes. In these contests, each player chooses a performance level or score. The first prize is awarded to the player with the highest score,the second,less valuable prize to the player with the second highest score, etc. Players are asymmetric in that they incur di¤erent costs of score. The players are assumed to have ordered marginal costs, and the prize sequence is assumed to be either quadratic or geometric. I show that each such contest has a unique Nash equilibrium and exhibit an algorithm that constructs the equilibrium. I then apply the main result to study: (a) the issue of tracking students in schools, (b) the incentive e¤ects of superstars,and (c)the optimality of winner-take-all contests.