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Monotone Comparative Statics for Games with Strategic Substitutes

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  • Roy, Sunanda
  • Sabarwal, Tarun

Abstract

This paper studies comparative statics of equilibria in models where the optimal responses under consideration are (weakly) decreasing in endogenous variables, and (weakly) increasing in exogenous parameters. Such models include parameterized games of strategic substitutes. The analysis provides a sufficient condition for existence of increasing equilibria at a higher parameter value. This condition is presented first for best-response functions; it can be translated easily to payoff functions with one-dimensional individual strategy spaces, and it has a natural analogue to best-response correspondences. The condition is tight in the sense that with a weakenened condition, the same result may not obtain. The results here apply to asymmetric equilibria, and are applied to two classes of examples -- Cournot duopoly and tournaments. Moreover, sufficient conditions are presented to exhibit strong comparative statics of equilibria (that is, every equilibrium at a higher parameter value is greater than a given equilibrium at a lower parameter value), and to show existence of increasing equilibrium selections.

Suggested Citation

  • Roy, Sunanda & Sabarwal, Tarun, 2005. "Monotone Comparative Statics for Games with Strategic Substitutes," MPRA Paper 4709, University Library of Munich, Germany, revised 04 Sep 2007.
  • Handle: RePEc:pra:mprapa:4709
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    More about this item

    Keywords

    Monotone comparative statics; Weakly decreasing functions; Strategic substitutes; Payoff functions;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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