The long run outcomes and global dynamics of a duopoly game with misspecified demand functions

International Game Theory Review

Volumn 6, Issue 3, 2004, Pages 343-379

  Bischi, Gian Italo ^a   Chiarella, Carl ^b   Kopel, Michael ^c  

^a UNIVERSITY OF URBINO   (Italy)

^b UNIVERSITY OF TECHNOLOGY SYDNEY   (Australia)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Bifurcations; Bounded rationality; Misspecified demand (function); Oligopoly games; Self confirming steady states

Indexed keywords

EID: 12844259646     PISSN: 02191989     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219198904000253     Document Type: Article

References (40)

1. Abraham, R., Gardini, L. and Mira, C. [1997] Chaos in Discrete Dynamical Systems (A Visual Introduction in Two Dimensions) (Springer-Verlag).
2. Bischi, G. I., Mammana, C. and Gardini, L. [2000] "Multistability and cyclic attractors in duopoly games," Chaos, Solitons and Fractals 11, 543-564.
3. Bischi, G. I. and Kopel, M. [2001] "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior and Organization 46(1), 73-100.
4. Bischi, G.-I., Gallegati, M. and Naimzada, A. [1999] "Symmetry- breaking bifurcations and representative firm in dynamic duopoly games," Annals of Operations Research 89, 253-272.
5. Brousseau, V. and Kirman, A. [1992] "Apparent convergence of learning processes in mis-specified games," in Game Theory and Economic Applications, eds. Dutta, B., Mookherjee, D., Partasarathy, T., Raghavan, T. E. S., Ray, D. and Tijs, S. (Springer), 303-331.
6. Brousseau, V. and Kirman, A. [1993] "The dynamics of learning in N-person games with the wrong N," in Frontiers of Game Theory, eds. Binmore, K., Kirman, A. and Tani, P. (MIT Press), 71-93.
7. Bulow, J. I., Geanakoplos, J. D. and Klemperer, P. D. [1985a] "Multimarket oligopoly: Strategic substitutes and complements," Journal of Political Economy 93, 488-511.
8. Bulow, J. I., Geanakoplos, J. D. and Klemperer, P. D. [1985b] "Holding the capacity to deter entry," The Economic Journal 95, 178-182.
9. Canovas, J. S. [2000] "Chaos in duopoly games," Nonlinear Studies 1(1), 97-104.
10. Canovas, J. S. and Linero, A. [2001] "Topological dynamic classification of duopoly games," Chaos, Solitons & Fractals 1(12), 1259-1266.
11. Chiarella, C. and Szidarovszky, F. [2001] "The nonlinear cournot model under uncertainty with continuously distributed time lags," Central European Journal of Operations Research 9, 183-196.
12. Chiarella, C., Szidarovszky, F. and Zhu, P. [2002] "The interaction of uncertainty and information lags in the cournot oligopoly model," in Oligopoly Dynamics; Models and Tools, eds. Puu, T. and Sushko, I. (Springer-Verlag), 233-263.
13. Dana, R. A. and Montrucchio, L. [1986] "Dynamic complexity in duopoly games," Journal of Economic Theory 40, 40-56.
14. Fudenberg, D. and Levine, D. [1998] The Theory of Learning in Games (MIT Press).
15. Gates, D. J., Rickard, J. A. and Wilson, D. J. [1978] "Convergence of a related game strategy," Journal of Mathematical Economics 5, 97-110.
16. Gates, D. J., Rickard, J. A. and Wilson, D. J. [1982] "Exact cooperative solution of a duopoly model without cooperation," Journal of Mathematical Economics 9, 27-35.
17. Gumowski, I. and Mira, C. [1980] Dynamique Chaotique, Cepadues editions (Toulose).
18. Huang, W. [2001] "Theory of adaptive adjustment," Discrete Dynamics in Nature and Society 5, 247-263.
19. Huck, S., Normann, H.-T. and Oechssler, J. [1999] "Learning in cournot oligopoly - an experiment," The Economic Journal 109(454), C80-C95.
20. Kirman, A. P. [1975] "Learning by firms about demand conditions," in Adaptive Economic Models, eds. Day, R. H. and Groves, T. (Academic Press), 137-156.
21. Kirman, A. P. [1983] "On mistaken beliefs and resultant equilibria," in Individual Forecasting and Aggregate Outcomes, eds. Frydman, R. and Phelps, E. S. (Cambridge University Press), 147-166.
22. Kirman, A. P. [1995]) "Learning in oligopoly: Theory, simulation, and experimental evidence," in Learning and Rationality in Economics, eds. Kirman, A. and Salmon, M. (Blackwell), 127-178.
23. Kirman, A. P. and Salmon, M. (eds.) [1995] Learning and Rationality in Economics (Blackwell).
24. Kopel, M. [1996] "Simple and complex adjustment dynamics in cournot duopoly models," Chaos, Solitons & Fractals 7(12), 2031-2048.
25. Kopel, M., Bischi, G.-I. and Gardini, L. [2000] "On new phenomena in dynamic promotional competition models with homogeneous and quasi-homogeneous firms," in Interaction and Market Structure. Essays on Heterogeneity in Economics, eds. Delli Gatti, D., Gallegati, M. and Kirman, A. P. (Springer-Verlag), 57-87.
26. Léonard, D. and Nishimura, K. [1999] "Nonlinear dynamics in the Cournot model without full information," Annals of Operations Research 89, 165-173.
27. Marimon, R. [1997] "Learning from learning in economics," in Advances in Economics and Econometrics, eds. Kreps, D. and Wallis, K. (Cambridge University Press).
28. Medio, A. and Lines, M. [2001] Nonlinear Dynamics (Cambridge University Press).
29. Mira, C., Gardini, L., Barugola,, A. and Cathala, J. C. [1996a] Chaotic Dynamics in Two-Dimensional Noninvertible Maps (World Scientific, Singapore).
30. Mira, C., Carcasses, J. P., Gilles, M. and Gardini, L. [1996b] "Plane foliation of two dimensional noninvertible maps," International Journal of Bifurcation and Chaos 6(8), 1439-1462.
31. Poston, T. and Stewart, I. [1978] Catastrophe Theory and its Applications (Pitman).
32. Puu, T. [1991] "Chaos in duopoly pricing," Chaos, Solitons & Fractals 1(6), 573-581.
33. Rand, D. [1978] "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics 5, 173-184.
34. Rassenti, S., Reynolds, S. S., Smith, V. L. and Szidarovszky, F. [2000] "Adaptation and convergence in repeated experimental cournot games," Journal of Economic Behavior and Organization 41, 117-146.
35. Schaffer, S. [1984] "Chaos, naivete, and consistent conjectures," Economics Letters 14, 155-162.
36. Schinkel, M. P., Tuinstra, J. and Vermeulen, D. [2002] "Convergence of Bayesian learning to general equilibrium in mis-specified models," Journal of Mathematical Economics 38, 483-508.
37. Szidarovszky, F. and Krawczyk, J. [2003] "On stable learning in dynamic oligopolies," Working paper, Department of Industrial Engineerig, University of Arizona.
38. Van Huyck, J. B., Cook, J. P. and Battalio, R. C. [1994] "Selection dynamics, asymptotic stability, and adaptive behavior," Journal of Political Economy 102, 975-1005.
39. Van Witteloostuijn, A. and Van Lier, A. [1990] "Chaotic patterns in Cournot competition," Metroeconomica 41, 161-185.
40. Wenzelburger, J. [2003] "Learning to play best response," forthcoming in International Game Theory Review.