Abstract We study contests in which there are multiple alternative public-good/bad prizes, and the players compete, by expending irreversible effort, over which prize to have awarded to them. Each prize may be a public good for some players and a public bad for the others, and the players expend their effort simultaneously and independently. We first prove the existence of a pure-strategy Nash equilibrium of the game, then establish when the total effort level expended for each prize is unique across the Nash equilibria, and then summarize and highlight other interesting and important properties of the equilibria. Finally, we discuss the effects of heterogeneity of valuations on the players’ equilibrium effort levels and a possible extension of the model.

中文翻译：

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具有多个替代奖品的竞赛：公共好/坏奖品和外部性

摘要 我们研究了有多种不同的公共好/坏奖品的竞赛，并且玩家通过付出不可逆转的努力来竞争授予他们的奖品。每个奖品对一些玩家来说可能是一种公共物品，而对另一些玩家来说可能是一种公共物品，玩家同时独立地花费他们的努力。我们首先证明了博弈的纯策略纳什均衡的存在，然后确定每个奖金花费的总努力水平在纳什均衡中何时是唯一的，然后总结并强调均衡的其他有趣和重要的属性。最后，我们讨论了估值异质性对参与者均衡努力水平的影响以及模型的可能扩展。