A price adjustment process in a model of monopolistic competition

International Game Theory Review

Volumn 6, Issue 3, 2004, Pages 417-442

  Tuinstra, Jan ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Bertrand competition; Bifurcation theory; Nonlinear oligopoly dynamics; Price adjustment

Indexed keywords

EID: 12844281978     PISSN: 02191989     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219198904000289     Document Type: Article

References (40)

1. Arrow, K. J. [1959] "Towards a theory of price adjustment," in The Allocation of Economic Resources, Abramowitz, M. et al. (Stanford University Press, Stanford).
2. Arrow, K. J. and Hurwicz, L. [1958] "On the stability of the competitive equilibrium, I," Econometrica 26, 522-552.
3. Arrow, K. J., Block, H. D. and Hurwicz, L. [1959] "On the stability of the competitive equilibrium, II," Econometrica 27, 82-109.
4. Atkinson, K. E. [1989] An Introduction to Numerical Analysis (John Wiley & Sons, New York).
5. Benedicks, M. and Carleson, L. [1991] "The dynamics of the Hénon map," Annals of Mathematics 133, 73-169.
6. Bischi, G.-I. and Gardini, L. [1997] "Cycles and bifurcations in duopoly games," University of Urbino, working paper.
7. Bischi, G.-I. and Naimzada, A. [1999] "Global analysis of a dynamic duopoly game with bounded rationality," Advances in Dynamic Games and Applications 5, 361-385.
8. Bonanno, G. [1988] "Oligopoly equilibria when firms have local knowledge of demand," International Economic Review 29, 45-55.
9. Bonanno, G. and Zeeman, E. C. [1985] "Limited knowledge of demand and oligopoly equilibria," Journal of Economic Theory 35, 276-283.
10. Brock, W. A. and Hommes, C. H. [1997] "A rational route to randomness," Econometrica 65, 1059-1095.
11. Corchón, L. C. and Mas-Colell, A. [1996] "On the stability of best reply and gradient systems with applications to imperfectly competitive models," Economics Letters 51, 59-65.
12. Devaney, R. L. [1989] An Introduction to Chaotic Dynamical Systems (Addison-Wesley, Redwood City).
13. Droste, E., Hommes, C. H. and Tuinstra, J. [2002] "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior 40, 232-269.
14. Furth, D. [1986] "Stability and instability in oligopoly," Journal of Economic Theory 40, 197-228.
15. Gabszewicz, J. J. and Vial, J.-P. [1972] "Oligopoly 'a la, Cournot' in general equilibrium analysis," Journal of Economic Theory 4, 381-400.
16. Gary-Bobo, R. J. [1987] "Locally consistent oligopolistic equilibria are Cournot-Walras equilibria," Economics Letters 23, 217-221.
17. Goeree, J. K., Hommes, C. and Weddepohl, C. [1997] "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior and Organization 33, 395-410.
18. Golubitsky, M., Stewart, I. N. and Schaeffer, D. G. [1988] Singularities and Groups in Bifurcation Theory, Vol. II (Springer-Verlag, New York).
19. Guckenheimer, J. and Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York).
20. Kirman, A. P. [1995] "Learning in oligopoly: Theory, simulation, and experimental evidence," in Learning and Rationality in Economics, eds. Kirman, A. P. and Salman, M. (Blackwell, Oxford).
21. Kopel, M. [1997] "Simple and complex adjustment dynamics in Cournot duopoly models," Chaos, Solitons, and Fractals 7, 2031-2048.
22. Kuznetsov, Yu. A. [1995] Elements of Applied Bifurcation Theory (Springer-Verlag, New York).
23. Mora, L. and Viana, M. [1993] "Abundance of strange attractors," Acta Mathematica 171, 1-71.
24. Negishi, T. [1961] "Monopolistic competition and general equilibrium," Review of Economic Studies 27, 136-139.
25. Newhouse, S. [1974] "Diffeomorphisms with infinitely many sinks," Topology 13, 9-18.
26. Newhouse, S. [1979] "The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms," Publ. Math. I.H.E.S. 50, 101-151.
27. Nikaido, H. [1975] Monopolistic Competition and Effective Demand (Princeton University Press).
28. Palis, J. and Takens, F. [1993] Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations (Cambridge University Press, Cambridge).
29. Rand, D. [1978] "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics 5, 173-184.
30. Roberts, D. J. and Sonnenschein, H. [1977] "On the foundations of the theory of monopolistic competition," Econometrica 45, 101-114.
31. Saari, D. G. and Simon, C. P. [1978] "Effective price mechanisms," Econometrica 46, 1097-1125.
32. Schinkel, M. P. [2001] Disequilibrium Theory. Reflections towards a Revival of Learning, Ph.D. Thesis, Universiteit Maastricht.
33. Schinkel, M. P., Tuinstra, J. and Vermeulen, D. [2000] "Convergence of Bayesian learning to general equilibrium in misspecified models," Journal of Mathematical Economics 38, 483-508.
34. Silvestre, J. [1977] "A model of general equilibrium with monopolistic behavior," Journal of Economic Theory 16, 425-442.
35. Smale, S. [1976] "A convergent process of price adjustment and global Newton methods," Journal of Mathematical Economics 3, 107-120.
36. Sonnenschein, H. [1973] "Do Walras' identity and continuity characterize the class of community excess demand functions?" Journal of Economic Theory 6, 345-354.
37. Takayama, A. [1985] Mathematical Economics, 2nd edition (Cambridge University Press, Cambridge).
38. Tuinstra, J. [2000] "A discrete and symmetric price adjustment process on the simplex," Journal of Economic Dynamics and Control 24, 881-907.
39. de Vilder, R. [1996] "Complicated endogenous business cycles undergross substitutability," Journal of Economic Theory 71, 416-442.
40. Yorke, J. A. and Alligood, K. T. [1983] "Cascades of period doubling bifurcations: A prerequisite for horseshoes," Bulletin American Mathematical Society 9, 319-322.