DP11592 | The Optimal Allocation of Punishments in Tullock Contests


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We study the role of punishments in Tullock contests with symmetric players. We first characterize the players' equilibrium strategies in a contest with either multiple identical prizes or multiple identical punishments (negative prizes). Given that a prize and a punishment have the same absolute value, we show that if the number of prizes is equal to the number of punishments and is lower (higher) than or equal to half the number of players, a designer who wishes to maximize the players' efforts will prefer to allocate punishments (prizes) over prizes (punishments). We also demonstrate that if the sum of the punishments is constrained, then in a contest without an exit option for the players, it is optimal for the designer who maximizes the players' efforts to allocate a single punishment that is equal to the punishment sum. However, in a contest with an exit option the optimal number of punishments depends on the value of the punishment sum and, in particular, the optimal number of punishments does not monotonically increase in the value of the punishment sum.