Contests with Prize Contracts

We analyze two-stage contests with symmetric players. During the rst stage, each player can receive a prize contract, which includes both a losing and winning prize with the same prize sum. After receiving their prize contracts, and no player wishes to change them due to the allocation of the other prize contracts, the players compete in the standard Tullock contest during the second stage. We show that in the subgame perfect equilibrium, if players participate in the second stage, they should receive multiple types of prize contracts. While the designer cannot achieve the optimal value of the players total e⁄ort in equilibrium, we demonstrate that if there are at least ve players, he can achieve the optimal value of the players highest e⁄ort in equilibrium by using two types of prize contracts.