We study the optimal design of round-robin tournaments with three symmetric players. We characterize the subgame-perfect equilibrium in these tournaments with either one or two prizes. Our results show that the players who wish to maximize their expected payoffs or their probabilities of winning have different preferences about the order of games under tournaments with one or two prizes. We analyze the optimal allocations of players for a designer who wishes to maximize the players’ expected total effort in the tournaments with one and two prizes, and by comparing between them, it is demonstrated that in order to maximize the players’ expected total effort the designer should allocate only one prize.

中文翻译：

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三人循环赛的优化设计

我们研究了三个对称玩家的循环赛的优化设计。我们用一个或两个奖项来描述这些锦标赛中的子博弈完美均衡。我们的结果表明，希望最大化其预期收益或获胜概率的玩家对具有一两个奖项的锦标赛的游戏顺序有不同的偏好。我们分析了希望在一奖和二奖的比赛中最大化玩家预期总努力的设计师的最佳玩家分配，并通过它们之间的比较，证明为了最大化玩家的预期总努力，设计师应该只分配一个奖项。