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Monotone comparative statics: Changes in preferences vs changes in the feasible set

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  • Kukushkin, Nikolai S.

Abstract

Let a preference ordering on a lattice be perturbed. As is well known, single crossing conditions are necessary and sufficient for a monotone reaction of the set of optimal choices from every chain. Actually, there are several interpretations of monotonicity and several corresponding single crossing conditions. We describe restrictions on the preferences that ensure a monotone reaction of the set of optimal choices from every sublattice whenever a perturbation of preferences satisfies the corresponding single crossing condition. Quasisupermodularity is necessary if we want monotonicity in every conceivable sense; otherwise, weaker conditions will do.

Suggested Citation

  • Kukushkin, Nikolai S., 2011. "Monotone comparative statics: Changes in preferences vs changes in the feasible set," MPRA Paper 31612, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31612
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    File URL: https://mpra.ub.uni-muenchen.de/31612/1/MPRA_paper_31612.pdf
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    References listed on IDEAS

    as
    1. Philip J. Reny, 2011. "On the Existence of Monotone Pure‐Strategy Equilibria in Bayesian Games," Econometrica, Econometric Society, vol. 79(2), pages 499-553, March.
    2. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    3. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
    4. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    7. Agliardi, Elettra, 2000. "A generalization of supermodularity," Economics Letters, Elsevier, vol. 68(3), pages 251-254, September.
    8. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    9. Bruno Strulovici & Thomas Weber, 2010. "Generalized monotonicity analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 377-406, June.
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    More about this item

    Keywords

    strategic complementarity; monotone comparative statics; best response correspondence; single crossing; quasisupermodularity;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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