# DP9908 All-pay auctions with certain and uncertain prizes

Author(s): | Yizhaq Minchuk, Aner Sela |

Publication Date: | March 2014 |

Keyword(s): | All-pay auctions, contests, uncertain prizes |

JEL(s): | D44, D82, J31, J41 |

Programme Areas: | Industrial Organization |

Link to this Page: | cepr.org/active/publications/discussion_papers/dp.php?dpno=9908 |

We study all-pay auctions with multiple prizes. The players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value. We characterize the equilibrium strategy and show that if the number of prizes is smaller than the number of players, independent of the ranking of the uncertain prize, a player's probability to win as well as his expected utility increases in his value for this prize. We demonstrate that a stochastic dominance relation between two distribution functions of the players' private values may increase but also even decrease the players' ex-ante expected utility as well the players' expected total effort. Also, increasing the number of prizes may decrease the players' ex-ante expected utility. Thus, we may conclude that a larger number of prizes does not necessarily benefit the players in a contest.