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Monotone comparative statics with separable objective functions

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  • Christian Ewerhart

    (University of Zurich)

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.

Suggested Citation

  • Christian Ewerhart, 2010. "Monotone comparative statics with separable objective functions," Economics Bulletin, AccessEcon, vol. 30(3), pages 2259-2269.
    • Handle: RePEc:ebl:ecbull:eb-10-00260
    as

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    References listed on IDEAS

    as
    1. 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.
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    More about this item

    Keywords

    Increasing differences; separable objective function; single crossing property; quantity competition;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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