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A Note On Stability Of Best Reply And Gradient Systems With Applications To Imperfectly Competitive Models

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Author Info

  • Luis Corchón

    ()
    (Universidad de Alicante)

  • Andreu Mas-Colell

    (Harvard University)

Abstract

In this paper we present a general result on the convergence to an equilibrium of a class of dynamic adjustment procedures -which includes Gradient Systems and Best Reply Dynamics as special cases- when there are two players and strategy sets are one dimensional. We also show that there are no restrictions on the form of Gradient or Best Reply dynamics, even under strong restrictions on the functional form of both demand and costs. This implies that we can construct examples with three players where the above dynamical procedures yield chaotic behavior.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1995-18.pdf
File Function: Fisrt version / Primera version, 1995
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1995-18.

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Length: 22 pages
Date of creation: Jul 1995
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1995-18

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Related research

Keywords: Stability; Chaotic Systems; Best Reply; Dynamics; Dominant Diagonal.;

References

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  1. Miguel Gines & Francisco Marhuenda, 1996. "Cost monotonic mechanisms," Investigaciones Economicas, Fundación SEPI, vol. 20(1), pages 89-103, January.
  2. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
  3. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer, vol. 1(1), pages 275-287, December.
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  5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  6. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
  8. Kennan, Donald & Rader, Trout, 1985. "Market Dynamics and the Law of Demand," Econometrica, Econometric Society, vol. 53(2), pages 465-71, March.
  9. Marhuenda, Francisco & Ortuno-Ortin, Ignacio, 1995. "Popular support for progressive taxation," Economics Letters, Elsevier, vol. 48(3-4), pages 319-324, June.
  10. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  11. Subir K. Chattopadhyay, 1996. "Pareto optimal improvements for sunspots: The golden rule as a target for stabilization," Economic Theory, Springer, vol. 8(1), pages 123-135.
  12. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
  13. Amparo Urbano Salvador & María Dolores Alepuz Domenech, 1994. "Market learning and price-dispersion," Working Papers. Serie AD 1994-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  14. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
  15. Marhuenda, F, 1995. "Distribution of Income and Aggregation of Demand," Econometrica, Econometric Society, vol. 63(3), pages 647-66, May.
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Cited by:
  1. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

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