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Success functions in large contests

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  • Azrieli, Yaron
  • Chambers, Christopher P.

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

Suggested Citation

  • Azrieli, Yaron & Chambers, Christopher P., 2026. "Success functions in large contests," Games and Economic Behavior, Elsevier, vol. 157(C), pages 253-262.
    • Handle: RePEc:eee:gamebe:v:157:y:2026:i:c:p:253-262
    DOI: 10.1016/j.geb.2026.02.004
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    2. Giovanni Valvassori Bolg`e, 2026. "Extreme Points and Large Contests," Papers 2601.19331, arXiv.org, revised Feb 2026.

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