Cahier 201907Titre :  Contests with an uncertain number of prizes  Résumé :  We study multipleprize contests where the number of prizes to be awarded is a random variable. We determine the symmetric Nash equilibrium of the contest game. We analyze the equilibrium outcome from the perspective of a contest designer aiming at maximizing the aggregate contest expenditure. Assuming that the total value at stake is nonincreasing in the number of prizes, we show that the aggregate contest expenditure decreases with the expectation on the number of prizes (firstorder stochastic dominance), with the risk in the number of prizes (secondorder stochastic dominance), and increases with the number of contestants. We give sufficient conditions such that the same holds under a general specification. Accordingly, a contest designer aiming at maximizing the aggregate contest expenditure should always award a single prize, reveal this information to the contestants and open the contest game to all potential participants.  Mot(s) clé :  Contest model Â· Rentseeking Â· Multipleprizes Â· Number uncertainty Â· Incomplete information  Title:  Contests with an uncertain number of prizes  Abstract:  We study multipleprize contests where the number of prizes to be awarded is a random variable. We determine the symmetric Nash equilibrium of the contest game. We analyze the equilibrium outcome from the perspective of a contest designer aiming at maximizing the aggregate contest expenditure. Assuming that the total value at stake is nonincreasing in the number of prizes, we show that the aggregate contest expenditure decreases with the expectation on the number of prizes (firstorder stochastic dominance), with the risk in the number of prizes (secondorder stochastic dominance), and increases with the number of contestants. We give sufficient conditions such that the same holds under a general specification. Accordingly, a contest designer aiming at maximizing the aggregate contest expenditure should always award a single prize, reveal this information to the contestants and open the contest game to all potential participants.  Keyword(s):  Contest model Â· Rentseeking Â· Multipleprizes Â· Number uncertainty Â· Incomplete information  Auteur(s) :  FranÃ§ois Maublanc, SÃ©bastien Rouillon  JEL Class.:  C7, D4, D7, D8  Télécharger le cahier Retour à la liste des Cahier du GRETHA (2019) 
