Games and Economic Behavior · 2026 · Yaron Azrieli、Christopher P. Chambers
中文摘要
我们考虑参与者为大集合（连续统）的竞赛，并对竞赛成功函数进行公理化刻画；这类成功函数产生于如下情形：表现由努力与一个随机因素共同构成，且胜者是那些表现超过由设计者预算约束所决定的截断值的人。任何此类随机表现函数（Random Performance Function, RPF）均满足共单调性（Co-monotonicity）性质，该性质意味着可以依据竞争性的强弱对对手的努力分布进行无歧义的排序。我们证明，共单调性连同标准的连续性与单调性性质，实际上刻画了RPF这一类函数。我们还给出了噪声项具有可加结构的充要条件。“交易者连续统的想法在读者看来或许显得怪异。实际上，它并不比连续统的价格、连续统的策略，或流体力学中连续统的‘粒子’更奇怪……应当强调，我们考虑交易者连续统并非仅仅是数学练习，而是一种经济思想的表达。”出自：Markets with a continuum of traders（《具有连续统交易者的市场》），Robert J. Aumann，Econometrica 1964年。
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 ‘particles’ 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