Revenue in contests with many participants

We show that in a contest with many participants and a single prize, the expected e¤ort (or resources) made by a participant whose evaluation of the prize is ranked as the kth highest valuation obeys an exponential rule in the limit and is equal to 1=2k of the total expected e¤ort made by all of the participants. Thus, even if the contest’s organizer can recover only k of the highest e¤ort, the total losses caused in the limit by the lost e¤orts is 1=2k+1 of all of the e¤orts. We also extend our results to contests with m prizes and with risk averse participants. Keywords: contest, all-pay auction, revenue, risk aversion. JEL classi…cation: D44, D82. Department of Industrial Engineering and Management, Faculty of Engineering Sciences, Ben-Gurion University, P.O. Box 653, Beer-Sheva 84105, Israel, [email protected] yDepartment of Industrial Engineering and Management, Faculty of Engineering Sciences, Ben-Gurion University, P.O. Box 653, Beer-Sheva 84105, Israel, [email protected]