Aggregating the single crossing property: theory and applications to comparative statics and Bayesian games
AbstractThe 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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Bibliographic InfoPaper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 493.
Date of creation: 01 Jun 2010
Date of revision:
Monotone comparative statics; Single crossing property; Bayesian games; Monotone strategies; First-price auctions; Logsupermodularity;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- D42 - Microeconomics - - Market Structure and Pricing - - - Monopoly
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-07-10 (All new papers)
- NEP-GTH-2010-07-10 (Game Theory)
- NEP-ORE-2010-07-10 (Operations Research)
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, 2007.
"Monotone equilibria in Bayesian games of strategic complementarities,"
Journal of Economic Theory,
Elsevier, vol. 134(1), pages 339-360, May.
- Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
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