Working Paper: CEPR ID: DP9908
Authors: Yizhaq Minchuk; Aner Sela
Abstract: 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.
Keywords: allpay auctions; contests; uncertain prizes
JEL Codes: D44; D82; J31; J41
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| number of prizes (m) < number of players (n) (C72) | probability of winning increases with value for uncertain prize (D81) |
| number of additional prizes (D44) | expected utility (D81) |
| stochastic dominance (D81) | expected utilities (D11) |