Cahier 2019-07

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

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