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On the stability of best reply and gradient systems with application to imperfectly competitive models

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  • Corchón, Luis C.
  • Mas-Colell, A.

Abstract

We present a general result on the convergence to an equilibrium of 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 the 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://e-archivo.uc3m.es/bitstream/10016/3812/1/CORCHON_1996_51_CL_ps.pdf
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Bibliographic Info

Paper provided by Universidad Carlos III de Madrid in its series Open Access publications from Universidad Carlos III de Madrid with number info:hdl:10016/3812.

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Length: 67 p.
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Handle: RePEc:ner:carlos:info:hdl:10016/3812

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Web page: http://www.uc3m.es

Related research

Keywords: Gradient; Best reply; Chaos; Stability;

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  1. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  2. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
  3. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
  4. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
  5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  6. Dana, Rose-Anne & Montrucchio, Luigi, 1987. "On rational dynamic strategies in infinite horizon models where agents discount the future," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 497-511, September.
  7. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-63, May.
  8. Kennan, Donald & Rader, Trout, 1985. "Market Dynamics and the Law of Demand," Econometrica, Econometric Society, vol. 53(2), pages 465-71, March.
  9. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
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Cited by:
  1. Eckart Jäger, 1999. "Exchange rates and bertrand oligopoly," Journal of Economics, Springer, vol. 70(3), pages 281-307, October.
  2. Cabrales, Antonio & Calvó-Armengol, Antoni & Zenou, Yves, 2011. "Social interactions and spillovers," Games and Economic Behavior, Elsevier, vol. 72(2), pages 339-360, June.
  3. Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  4. Furth, D., 2007. "Anything goes with heterogeneous, but not with homogeneous oligopoly," CeNDEF Working Papers 07-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  5. Dziubinski, Marcin & Roy, Jaideep, 2007. "Endogenous selection of aspiring and rational rules in coordination games," MPRA Paper 5941, University Library of Munich, Germany.
  6. Ahmad Naimzada & Fabio Tramontana, 2010. "A Dynamic Model of a Boundedly Rational Consumer with a Simple Least Squared Learning Mechanism," Computational Economics, Society for Computational Economics, vol. 36(1), pages 47-56, June.
  7. Furth, Dave, 2009. "Anything goes with heterogeneous, but not always with homogeneous oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 183-203, January.
  8. Ahmad K. Naimzada & Fabio Tramontana, 2007. "Un Modello Dinamico del Consumatore con Razionalità Limitata e Analisi Globale," Working Papers 117, University of Milano-Bicocca, Department of Economics, revised 2007.
  9. Marc Escrihuela, 2002. "Cartel Sustainability And Cartel Stability," Working Papers. Serie AD 2002-16, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Dindos, Martin & Mezzetti, Claudio, 2006. "Better-reply dynamics and global convergence to Nash equilibrium in aggregative games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 261-292, February.
  11. Naimzada Ahmad K. & Tramontana Fabio, 2008. "A Dynamic Model of a Boundedly Rational Consumer and Global Analysis," Economia politica, Società editrice il Mulino, issue 1, pages 59-94.

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