In contest settings, heterogeneity between contestants generally leads to low effort provision, and many instruments have been suggested to restore competitive balance. We suggest that heterogeneity may evolve depending upon the outcome of previous contests. Restoring competitive balance in this setting is challenging, and we consider the choice faced by a principal who can distribute a prize fund over two consecutive all-pay auction contests. Contestants are heterogeneous in the sense that one of them has a head start in the first contest. The winner of contest one gains the stage prize and a net head start in contest two; the size of this net head start also varies between players. The head start of the early leader can be increased, neutralized or overturned. The principal aims to maximize total effort. We show how the potential head start that the initial underdog can gain is critical in determining expected efforts. When this parameter is small, the principal can do no better than running a single contest. When the initial underdog can catch up and surpass the first-contest favourite, there is scope to do better. Indeed, it is possible to completely neutralize the initial heterogeneity and capture all of the surplus from the players, inciting a level of expected effort equal to the prize value. Competitive balance is achieved by a judicious division of the prize budget.

在比赛环境中，参赛者之间的异质性通常会导致提供省力的方法，并且已经提出了许多手段来恢复竞争平衡。我们建议异质性可能会根据先前比赛的结果而演变。在这种情况下恢复竞争平衡是一项挑战，我们认为校长面临的选择是谁可以在连续的两次全薪拍卖比赛中分配奖金。参赛者是异类的，因为他们中的一个人在第一场比赛中拥有领先优势。竞赛一的获胜者获得舞台奖，并在竞赛二中获得净领先。每个球员的净头距大小也有所不同。早期领导者的领先优势可以增加，抵消或推翻。校长的目标是最大程度地努力。我们展示了初始失败者可以获得的潜在领先优势对于确定预期的工作至关重要。如果此参数较小，则校长不能比举办单个竞赛更好。当最初的劣势者能够赶上并超过首个竞赛的最爱时，就有了做得更好的空间。实际上，有可能完全抵消最初的异质性并从玩家手中夺走所有剩余资金，从而激发出与奖品价值相等的预期努力水平。竞争性平衡是通过明智地分配奖金预算来实现的。实际上，有可能完全抵消最初的异质性并从玩家手中夺走所有剩余资金，从而激发出与奖品价值相等的预期努力水平。竞争性平衡是通过明智地分配奖金预算来实现的。实际上，有可能完全抵消最初的异质性并从玩家手中夺走所有剩余资金，从而激发出与奖品价值相等的预期努力水平。竞争性平衡是通过明智地分配奖金预算来实现的。