We prove the existence of a behavioral-strategy Bayesian Nash equilibrium in contests where each contestant’s probability to win is continuous in efforts outside the zero-effort profile, monotone in his own effort, and greater that 1/2 if that contestant is the only one exerting positive effort. General type spaces, and in particular a continuum of information types, are allowed. As a corollary, the existence of a pure-strategy Bayesian Nash equilibrium is established in generalized Tullock contests, where the probability to win is strictly concave in one’s own effort for any non-zero effort profile of other players.

中文翻译：

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在（几乎连续的）竞赛中存在贝叶斯纳什均衡

我们证明了竞赛中存在一种行为策略贝叶斯纳什均衡，其中每个参赛者的获胜概率在零努力状况之外的努力中是连续的，在他自己的努力中是单调的，如果该选手是唯一的，则大于1/2发挥积极的作用。允许使用通用类型空间，尤其是信息类型的连续体。作为推论，纯策略贝叶斯纳什均衡的存在是在广义的Tullock竞赛中建立的，对于其他玩家的任何非零努力状况，获胜的可能性完全取决于自己的努力。