We study two-stage elimination Tullock contests. In the first stage all the players compete against each other; then some advance to the second stage while the others are removed. The finalists compete against each other in the second stage, and one of them wins the prize. To maximize the expected total effort, the designer can give a head start to the winner of the first stage when he competes against the other finalists in the second stage. We show that the optimal head start, independent of the number of finalists, always increases the players’ expected total effort. We also show how the number of players and finalists affect the value of the optimal head start.

中文翻译：

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最佳淘汰赛的两阶段淘汰赛

我们研究了两阶段淘汰塔洛克比赛。在第一阶段，所有玩家都互相竞争。然后其中一些进入第二阶段，而其他阶段则被删除。决赛入围者在第二阶段相互竞争，其中一名赢得了大奖。为了最大程度地提高预期的总工作量，设计师可以在第二阶段与其他决赛入围者竞争时为第一阶段的获胜者抢先一步。我们显示出最佳的起点，独立于决赛选手的人数，总是会增加玩家的期望总努力。我们还将展示玩家和决赛选手的数量如何影响最佳抢先开始的价值。