A Note On Stability Of Best Reply And Gradient Systems With Applications To Imperfectly Competitive Models
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.
|Date of creation:||Jul 1995|
|Publication status:||Published by Ivie|
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- Marhuenda, Francisco & Ortuno-Ortin, Ignacio, 1995. "Popular support for progressive taxation," Economics Letters, Elsevier, vol. 48(3-4), pages 319-324, June.
- Subir K. Chattopadhyay, 1996. "Pareto optimal improvements for sunspots: The golden rule as a target for stabilization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 123-135.
- Miguel Gines & Francisco Marhuenda, 1996.
"Cost monotonic mechanisms,"
Fundación SEPI, vol. 20(1), pages 89-103, January.
- Miguel Ginés Vilar & Francisco Marhuenda, 1995. "Cost Monotonic Mecanisms," Working Papers. Serie AD 1995-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
- José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- 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.
- A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
- 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).
- K. Okuguchi, 1964. "The Stability of The Cournot Oligopoly Solution: A Further Generalization," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 143-146.
- 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.
- Kennan, Donald & Rader, Trout, 1985. "Market Dynamics and the Law of Demand," Econometrica, Econometric Society, vol. 53(2), pages 465-471, March.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
- José Alcalde, 1995. "Exchange-Proofness or Divorce-Proofness? Stability in One-Sided Matching Markets," Working Papers. Serie AD 1995-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
- Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier.
- Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
- Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
- F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," Review of Economic Studies, Oxford University Press, vol. 29(4), pages 329-331.
- Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
- Marhuenda, F, 1995. "Distribution of Income and Aggregation of Demand," Econometrica, Econometric Society, vol. 63(3), pages 647-666, May. Full references (including those not matched with items on IDEAS)
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