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Monotone comparative statics with separable objective functions

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  • Christian Ewerhart

Abstract

The sum of a supermodular function, assumed nondecreasing in the choice variable, and of a 'concavely supermodularizable' function, assumed nonincreasing in the parameter variable, satisfies the Milgrom-Shannon (1994, Monotone comparative statics, Econometrica 62, 157-180) single crossing condition. As an application, I prove existence of a pure strategy Nash equilibrium in a Cournot duopoly with logconcave demand, affiliated types, and nondecreasing costs.

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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 472.

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Date of creation: Jan 2010
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Handle: RePEc:zur:iewwpx:472

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Keywords: Supermodularity; separable objective function; single crossing condition; quantity competition.;

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  1. 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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