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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31612.

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Date of creation: 15 Jun 2011
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Handle: RePEc:pra:mprapa:31612

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

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  1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers, Stanford - Institute for Thoretical Economics 11, Stanford - Institute for Thoretical Economics.
  2. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, Elsevier, vol. 81(1), pages 201-219, July.
  3. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 69(4), pages 861-89, July.
  4. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, Econometric Society, vol. 75(2), pages 401-431, 03.
  5. Philip J Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," NajEcon Working Paper Reviews, www.najecon.org 784828000000000413, www.najecon.org.
  6. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  7. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, Springer, vol. 5(2), pages 209-27, March.
  8. Agliardi, Elettra, 2000. "A generalization of supermodularity," Economics Letters, Elsevier, Elsevier, vol. 68(3), pages 251-254, September.
  9. Bruno Strulovici & Thomas Weber, 2010. "Generalized monotonicity analysis," Economic Theory, Springer, Springer, vol. 43(3), pages 377-406, June.
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