Aggregating the single crossing property

John K.H. Quah*, Bruno Strulovici

*Corresponding author for this work

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

The single crossing property plays a crucial role in economic theory, yet there are important instances where the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum or convex combination of two functions with the single crossing property need not have that property. We introduce a new condition characterizing when the single crossing property is stable under aggregation, and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation. We use our results to establish properties of objective functions (convexity, logsupermodularity), the monotonicity of optimal decisions under uncertainty, and the existence of monotone equilibria in Bayesian games.

Original languageEnglish (US)
Pages (from-to)2333-2348
Number of pages16
JournalEconometrica
Volume80
Issue number5
DOIs
StatePublished - Sep 1 2012

Keywords

  • Bayesian games
  • Logsupermodularity
  • Monotone comparative statics
  • Monotone strategies
  • Signed-ratio monotonicity
  • Single crossing property

ASJC Scopus subject areas

  • Economics and Econometrics

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