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Comparative Statics by Adaptative Dynamics and the Correspondence Principle

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Author Info
Federico Echenique () (Departamento de Economía, Facultad de Ciencias Sociales, Universidad de la República and Department of Economics, University of California, Berkeley)

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Abstract

This paper formalizes the relation between comparative statics and the out-of-equilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o learning dynamics that involve larger values of the endogenous variables. Second, equilibrium selections that are not monotone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent.

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Publisher Info
Paper provided by Department of Economics - dECON in its series Documentos de Trabajo (working papers) with number 2099.

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Length: 37 pages
Date of creation: Dec 1999
Date of revision:
Handle: RePEc:ude:wpaper:2099

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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  1. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September. [Downloadable!] (restricted)
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November. [Downloadable!] (restricted)
  3. Joseph Farrell & Garth Saloner, 1985. "Standardization, Compatibility, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 16(1), pages 70-83, Spring. [Downloadable!] (restricted)
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  4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  5. Ausubel, Lawrence M & Deneckere, Raymond J, 1993. "A Generalized Theorem of the Maximum," Economic Theory, Springer, vol. 3(1), pages 99-107, January.
  6. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June. [Downloadable!] (restricted)
  7. Athey, S, 1996. "Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity," Working papers 96-22, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March. [Downloadable!] (restricted)
  9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  10. Milgrom, Paul R & Qian, Yingyi & Roberts, John, 1991. "Complementarities, Momentum, and the Evolution of Modern Manufacturing," American Economic Review, American Economic Association, vol. 81(2), pages 84-88, May. [Downloadable!] (restricted)
  11. Hatta, Tatsuo, 1980. "Structure of the Correspondence Principle at an Extremum Point," Review of Economic Studies, Blackwell Publishing, vol. 47(5), pages 987-97, October. [Downloadable!] (restricted)
  12. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February. [Downloadable!] (restricted)
  13. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August. [Downloadable!] (restricted)
  14. Lippman, Steven A. & Mamer, John W. & McCardle, Kevin F., 1987. "Comparative statics in non-cooperative games via transfinitely iterated play," Journal of Economic Theory, Elsevier, vol. 41(2), pages 288-303, April. [Downloadable!] (restricted)
  15. W. A. Brock, 1977. "Applications of Recent Results on the Asymptotic Stability of Optimal Control to the Problem of Comparing Long Run Equilibria," Discussion Papers 274, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  16. Magill, Michael J P & Scheinkman, Jose A, 1979. "Stability of Regular Equilibria and the Correspondence Principle for Symmetric Variational Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 297-315, June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Federico Echenique, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series 1020, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  2. Roy, Sunanda & Sabarwal, Tarun, 2006. "On the (non-)lattice structure of the equilibrium set in games with strategic substitutes," MPRA Paper 4120, University Library of Munich, Germany, revised 23 May 2007. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
    Other versions:
  4. Nabil Al-Najjar & Sandeep Baliga & David Besanko, 2005. "The Sunk Cost Bias and Managerial Pricing Practices," Levine's Bibliography 666156000000000496, UCLA Department of Economics. [Downloadable!]
    Other versions:
  5. Di Tella, Rafael & Dubra, Juan, 2006. "Crime and Punishment in the "American Dream"," MPRA Paper 500, University Library of Munich, Germany. [Downloadable!]
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  6. Mathevet, Laurent, 2007. "Supermodular Bayesian implementation: Learning and incentive design," Working Papers 1265, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  7. Woźny, Łukasz & Garbicz, Marek, 2005. "Taxes and labour supply under interdependent preferences," MPRA Paper 462, University Library of Munich, Germany, revised Jun 2005. [Downloadable!]
  8. Sunanda Roy & Tarun Sabarwal, 2005. "Comparative Statics with Never Increasing Correspondences," Game Theory and Information 0505001, EconWPA, revised 21 Oct 2005. [Downloadable!]
  9. Gunnar Nordén, 2004. "The Correspondence Principle and Structural Stability in Non-Maximum," Levine's Bibliography 122247000000000422, UCLA Department of Economics. [Downloadable!]
  10. AMIR, Rabah, 2003. "Supermodularity and complementarity in ecnomics: an elementary survey," CORE Discussion Papers 2003104, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  11. Sylvain Dessy & Jacques Ewoudou & Isabelle Ouellet, 2006. "Understanding the Persistent Low Performance of African Agriculture," Cahiers de recherche 0622, CIRPEE. [Downloadable!]
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