This paper studies a multi-prize imperfectly discriminatory contest with symmetric risk-averse contestants. Adopting a multi-winner nested Tullock contest model, we first establish the existence and uniqueness of a symmetric pure-strategy equilibrium under plausible conditions. We then investigate the optimal prize allocation in the contest. Our analysis provides a formal account of the incentive effects triggered by a variation in the prevailing prize structure when contestants are risk averse. We demonstrate that contestants' incentive subtly depends not only on the degree of a contestant's risk aversion but also that of his prudence. The former affects the marginal benefit of effort, while the latter affects the marginal cost. We derive sufficient conditions under which a single-(multi-)prize contest would be optimal when the contest designer aims to maximize total effort. We also discuss in depth the roles played by risk aversion and prudence in optimal prize allocation.

本文研究了具有对称风险规避竞赛者的多奖不完全歧视竞赛。采用多赢家嵌套塔洛克竞赛模型，我们首先在似是而非的条件下建立对称纯策略均衡的存在性和唯一性。然后我们调查比赛中的最佳奖品分配。我们的分析正式说明了当参赛者厌恶风险时，现行奖金结构的变化所引发的激励效应。我们证明，参赛者的激励微妙地不仅取决于参赛者的风险规避程度，还取决于他的审慎程度。前者影响努力的边际收益，而后者影响边际成本。我们推导出充分条件，当竞赛设计者的目标是最大化总努力时，单（多）奖竞赛将是最佳的。我们还深入讨论了风险规避和审慎在最佳奖金分配中所起的作用。