Abstract This paper examines optimally biased Tullock contests. We consider a multi-player Tullock contest in which players differ in their prize valuations. The designer is allowed to impose identity-dependent treatments – i.e., multiplicative biases – to vary their relative competitiveness. The literature has been limited, because a closed-form solution to the equilibrium is in general unavailable when the number of contestants exceeds two, which nullifies the usual implicit programming approach. We develop an algorithmic technique adapted from the general approach of Fu and Wu (2020) and obtain a closed-form solution to the optimum that addresses a broad array of design objectives. We further analyze a resource allocation problem in a research tournament and adapt Fu and Wu’s (2020) approach to this noncanonical setting. Our analysis paves the way for future research in this vein.

中文翻译：

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最优偏置的塔洛克竞赛

摘要 本文研究了最优偏置的 Tullock 竞赛。我们考虑一个多人 Tullock 比赛，其中玩家的奖金估值不同。设计者被允许施加依赖于身份的处理——即乘法偏差——来改变他们的相对竞争力。文献有限，因为当参赛者人数超过 2 人时，均衡的封闭形式解通常不可用，这使通常的隐式编程方法无效。我们开发了一种改编自 Fu 和 Wu (2020) 的一般方法的算法技术，并获得了解决广泛设计目标的最优方案的封闭形式解决方案。我们进一步分析了研究锦标赛中的资源分配问题，并将 Fu 和 Wu（2020）的方法应用于这种非规范环境。