We study Tullock contests with n symmetric players. We show that in a contest without an exit option, if prizes and punishments (negative prizes) have the same cost, it is optimal for the designer who wants to maximize the players’ total effort to allocate the entire prize sum to a single punishment without any prize. On the other hand, in a contest with an exit option, it is optimal to allocate the entire prize sum to a single prize and a single punishment, where independent of the costs of the prize and the punishment, the optimal value of the prize is larger than the optimal value of the punishment. We also show that allocating a prize and a punishment in a two-stage contest yields a higher expected total effort than in a one-stage contest.

中文翻译：

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塔洛克竞赛中奖惩的最优分配

我们研究了与 n 个对称玩家的 Tullock 比赛。我们表明，在没有退出选项的比赛中，如果奖品和惩罚（负奖）具有相同的成本，那么对于想要最大化玩家总努力的设计者来说，将整个奖金总和分配给单个惩罚是最佳的任何奖品。另一方面，在有退出选项的比赛中，最好将全部奖金分配给一个奖和一个惩罚，其中与奖和惩罚的成本无关，奖的最优价值是大于惩罚的最优值。我们还表明，在两阶段比赛中分配奖品和惩罚会产生比单阶段比赛更高的预期总努力。