Success functions in large contests

IF 1.1 3区经济学 Q3 ECONOMICS

Games and Economic Behavior Pub Date : 2026-03-01 Epub Date: 2026-02-14 DOI:10.1016/j.geb.2026.02.004

Yaron Azrieli , Christopher P. Chambers

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引用次数: 0

Abstract

We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a cutoff determined by the designer’s budget constraint. Any such Random Performance Function (RPF) satisfies a Co-monotonicity property, which implies that opponents’ effort distributions can be unambiguously ranked based on how competitive they are. We prove that Co-monotonicity, along with standard continuity and monotonicity properties, in fact characterize the class of RPFs. We also describe necessary and sufficient conditions for the noise term to have an additive structure. “The idea of a continuum of traders may seem outlandish to the reader. Actually, it is no stranger than a continuum of prices or of strategies or a continuum of <ddq>‘particles’</ddq> in fluid mechanics... It should be emphasized that our consideration of a continuum of traders is not merely a mathematical exercise; it is the expression of an economic idea.” In: Markets with a continuum of traders, Robert J. Aumann, Econometrica 1964

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成功在大型比赛中发挥作用

我们考虑具有大量参与者的比赛，并将比赛成功函数公式化，即当表现由努力和随机元素组成时，当表现超出设计师预算约束所决定的截止时间时，就会出现比赛成功函数。任何这样的随机性能函数（RPF）都满足共单调性，这意味着对手的努力分布可以根据他们的竞争程度进行明确的排名。我们证明了共单调性，以及标准连续性和单调性，实际上是rfp类的特征。我们还描述了噪声项具有加性结构的充分必要条件。在读者看来，交易员连续存在的想法可能有些古怪。实际上，这并不比流体力学中价格或策略的连续体或“粒子”的连续体更奇怪……应该强调的是，我们对交易员连续体的考虑不仅仅是一个数学练习；它是一种经济理念的表达。”见：《连续交易者的市场》，罗伯特·j·奥曼，《计量经济学》，1964

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来源期刊

Games and Economic Behavior ECONOMICS-

CiteScore

1.90

自引率

9.10%

发文量

148

期刊介绍： Games and Economic Behavior facilitates cross-fertilization between theories and applications of game theoretic reasoning. It consistently attracts the best quality and most creative papers in interdisciplinary studies within the social, biological, and mathematical sciences. Most readers recognize it as the leading journal in game theory. Research Areas Include: • Game theory • Economics • Political science • Biology • Computer science • Mathematics • Psychology