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Comparative Statics by Adaptive Dynamics and The Correspondence Principle

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  • Federico Echenique

    (University of California)

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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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1906.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1906

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  1. Milgrom, Paul R & Qian, Yingyi & Roberts, John, 1991. "Complementarities, Momentum, and the Evolution of Modern Manufacturing," American Economic Review, American Economic Association, American Economic Association, vol. 81(2), pages 84-88, May.
  2. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers, Stanford - Institute for Thoretical Economics 11, Stanford - Institute for Thoretical Economics.
  3. Hatta, Tatsuo, 1980. "Structure of the Correspondence Principle at an Extremum Point," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 47(5), pages 987-97, October.
  4. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, Elsevier, vol. 7(2), pages 295-300, September.
  5. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, American Economic Association, vol. 84(3), pages 441-59, June.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
  7. 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).
  8. 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, Northwestern University, Center for Mathematical Studies in Economics and Management Science 274, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Ausubel, Lawrence M & Deneckere, Raymond J, 1993. "A Generalized Theorem of the Maximum," Economic Theory, Springer, Springer, vol. 3(1), pages 99-107, January.
  10. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 42(2), pages 307-314, February.
  11. Athey, S, 1996. "Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 96-22, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 103(3), pages 441-63, August.
  13. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 297-315, June.
  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, Elsevier, vol. 41(2), pages 288-303, April.
  15. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1255-77, November.
  16. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, Elsevier, vol. 73(1), pages 183-198, March.
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