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Comparative Statics by Adaptive Dynamics and the Correspondence Principle

  • Federico Echenique


    (Microeconometric Research Division, Statistics Norway, P.B. 8131 Dep., 0033 Oslo, Norway)

Federico Echenique JEL#: C61, C62, C72, C73 Keywords: Monotone comparative statics, supermodularity, strategic complements, learning, correspondence principle 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 mono- tone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent. January 2000

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 2 (March)
Pages: 833-844

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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:2:p:833-844
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  1. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  2. 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.
  3. 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.
  4. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  5. 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.
  6. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February.
  7. Ausubel, Lawrence M & Deneckere, Raymond J, 1993. "A Generalized Theorem of the Maximum," Economic Theory, Springer, vol. 3(1), pages 99-107, January.
  8. 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.
  9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  10. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  11. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar, volume 0, number 1585, March.
  12. 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.
  13. Hatta, Tatsuo, 1980. "Structure of the Correspondence Principle at an Extremum Point," Review of Economic Studies, Wiley Blackwell, vol. 47(5), pages 987-97, October.
  14. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  15. 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.
  16. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  17. 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.
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