Cahier 2019-07| Titre : | Contests with an uncertain number of prizes | | Résumé : | We study multiple-prize 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 non-increasing in the number of prizes, we show that the aggregate contest expenditure decreases with the expectation on the number of prizes (first-order stochastic dominance), with the risk in the number of prizes (second-order 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 · Rent-seeking · Multiple-prizes · Number uncertainty · Incomplete information | | Title: | Contests with an uncertain number of prizes | | Abstract: | We study multiple-prize 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 non-increasing in the number of prizes, we show that the aggregate contest expenditure decreases with the expectation on the number of prizes (first-order stochastic dominance), with the risk in the number of prizes (second-order 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 · Rent-seeking · Multiple-prizes · Number uncertainty · Incomplete information | | Auteur(s) : | François Maublanc, Sébastien Rouillon | | JEL Class.: | C7, D4, D7, D8 | Télécharger le cahier Retour à la liste des Cahier du GRETHA (2019) |
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