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Contests with an uncertain number of prizes

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  • François Maublanc
  • Sébastien Rouillon

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.

Suggested Citation

  • François Maublanc & Sébastien Rouillon, 2019. "Contests with an uncertain number of prizes," Cahiers du GREThA (2007-2019) 2019-07, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    • Handle: RePEc:grt:wpegrt:2019-07
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    References listed on IDEAS

    as
    1. Nava Kahana & Doron Klunover, 2015. "A note on Poisson contests," Public Choice, Springer, vol. 165(1), pages 97-102, October.
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    More about this item

    Keywords

    Contest model · Rent-seeking · Multiple-prizes · Number uncertainty · Incomplete information;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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