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Aggregating the single crossing property: theory and applications to comparative statics and Bayesian games

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  • John Quah
  • Bruno Strulovici

Abstract

The single crossing property plays a crucial role in monotone comparative statics (Milgrom and Shannon (1994)), yet in some important applications the property cannot be directly assumed or easily derived.� Difficulties often arise because the property cannot be aggregated: the sum of two functions with the single crossing property need not have the same property.� We obtain the precise conditions under which functions with the single crossing property add up to functions with this property.� We apply our results to certain Bayesian games when establishing the monotonicity of strategies is an important step in proving equilibrium existence.� In particular, we find conditions under which first-price auctions have monotone equilibria, generalizing the result of Reny and Zamir (2004).

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File URL: http://www.economics.ox.ac.uk/materials/papers/4385/paper493.pdf
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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 493.

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Date of creation: 01 Jun 2010
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Handle: RePEc:oxf:wpaper:493

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Keywords: Monotone comparative statics; Single crossing property; Bayesian games; Monotone strategies; First-price auctions; Logsupermodularity;

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  1. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
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