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Monotone comparative statics with separable objective functions


Ewerhart, Christian (2010). Monotone comparative statics with separable objective functions. Economics Bulletin, 30(3):2259-2269.

Abstract

The Milgrom-Shannon single crossing property is essential for monotone comparative statics of optimization problems and noncooperative games. This paper formulates conditions for an additively separable objective function to satisfy the single crossing property. One component of the objective function is assumed to allow a monotone concave transformation with increasing differences, and to be nondecreasing in the parameter variable. The other component is assumed to exhibit increasing differences, and to be nonincreasing in the choice variable. As an application, I prove existence of an isotone pure strategy Nash equilibrium in a Cournot duopoly with logconcave demand, affiliated types, and nondecreasing costs.

Abstract

The Milgrom-Shannon single crossing property is essential for monotone comparative statics of optimization problems and noncooperative games. This paper formulates conditions for an additively separable objective function to satisfy the single crossing property. One component of the objective function is assumed to allow a monotone concave transformation with increasing differences, and to be nondecreasing in the parameter variable. The other component is assumed to exhibit increasing differences, and to be nonincreasing in the choice variable. As an application, I prove existence of an isotone pure strategy Nash equilibrium in a Cournot duopoly with logconcave demand, affiliated types, and nondecreasing costs.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
Language:English
Date:2010
Deposited On:02 Nov 2010 14:32
Last Modified:07 Dec 2017 04:17
Publisher:Economics Bulletin
ISSN:1545-2921
Official URL:http://www.accessecon.com/Pubs/EB/2010/Volume30/EB-10-V30-I3-P207.pdf

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