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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.

Suggested Citation

  • Christian Ewerhart, 2010. "Monotone comparative statics with separable objective functions," IEW - Working Papers 472, Institute for Empirical Research in Economics - University of Zurich.
  • Handle: RePEc:zur:iewwpx:472
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    File URL: http://www.econ.uzh.ch/static/wp_iew/iewwp472.pdf
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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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    Keywords

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

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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