Monotone Comparative Statics for Games with Strategic Substitutes

Sunanda Roy and Tarun Sabarwal ()

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Monotone comparative statics; Weakly decreasing functions; Strategic substitutes; Payoff functions (search for similar items in EconPapers)
JEL-codes: C60 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cse and nep-gth
Date: 2005-05, Revised 2007-09-04
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http://mpra.ub.uni-muenchen.de/4709/

Related works:
Working Paper: Monotone Comparative Statics for Games With Strategic Substitutes (2009)
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