Aggregating the single crossing property: theory and applications to comparative statics and Bayesian games
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).
|Date of creation:||01 Jun 2010|
|Date of revision:|
|Contact details of provider:|| Postal: Manor Rd. Building, Oxford, OX1 3UQ|
Web page: http://www.economics.ox.ac.uk/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Van Zandt, Timothy & Vives, Xavier, 2003.
"Monotone Equilibria in Bayesian Games of Strategic Complementarities,"
CEPR Discussion Papers
4103, C.E.P.R. Discussion Papers.
- 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.
When requesting a correction, please mention this item's handle: RePEc:oxf:wpaper:493. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Monica Birds)
If references are entirely missing, you can add them using this form.