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ralph lauren polo

Christian Ewerhart
''Monotone comparative statics with separable objective functions''
( 2010, Vol. 30 No.3 )
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.
Keywords: Increasing differences, separable objective function, single crossing property; quantity competition
JEL: C6 - Mathematical Methods and Programming: General
C7 - Game Theory and Bargaining Theory:General
Manuscript Received : Apr 18 2010 Manuscript Accepted : Aug 26 2010

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