Monotone comparative statics with separable objective functions
AbstractThe 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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Bibliographic InfoPaper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 472.
Date of creation: Jan 2010
Date of revision:
Supermodularity; separable objective function; single crossing condition; quantity competition.;
Other versions of this item:
- Christian Ewerhart, 2010. "Monotone comparative statics with separable objective functions," Economics Bulletin, AccessEcon, vol. 30(3), pages 2259-2269.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-17 (All new papers)
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- Van Zandt, Timothy & Vives, Xavier, 2003.
"Monotone Equilibria in Bayesian Games of Strategic Complementarities,"
CEPR Discussion Papers
4103, C.E.P.R. Discussion Papers.
- 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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