Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players
A heterogeneous Bertrand duopoly game with bounded rational and adaptive players manufacturing differentiated products is subject of investigation. The main goal is to demonstrate that participation of one bounded rational player in the game suffices to destabilize the duopoly. The game is modelled with a system of two difference equations. Evolution of prices over time is obtained by iteration of a two dimensional nonlinear map. Equilibria are found and local stability properties thereof are analyzed. Complex behavior of the system is examined by means of numerical simulations. Region of stability of the Nash equilibrium is demonstrated in the plane of the speeds of adjustment. Period doubling route to chaos is presented on the bifurcation diagrams and on the largest Lyapunov characteristic exponent graph. Lyapunov time is calculated. Chaotic attractors are depicted and their fractal dimensions are computed. Sensitive dependence on initial conditions is evidenced.
Volume (Year): 2 (2010)
Issue (Month): 2 (March)
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- Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, December.
- Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
- Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
- Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, December.
- Agiza, H.N. & Hegazi, A.S. & Elsadany, A.A., 2002. "Complex dynamics and synchronization of a duopoly game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 133-146.
- Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
- Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
- Onozaki, Tamotsu & Sieg, Gernot & Yokoo, Masanori, 2003. "Stability, chaos and multiple attractors: a single agent makes a difference," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1917-1938, August.
- Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
- Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
- G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
- Wouter J. Denhaan, 2000.
"The Importance Of The Number Of Different Agents In A Heterogeneous Asset-Pricing Model,"
Computing in Economics and Finance 2000
349, Society for Computational Economics.
- Den Haan, Wouter J., 2001. "The importance of the number of different agents in a heterogeneous asset-pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 721-746, May.
- Rothman, Philip, 1995. "Chaotic dynamics. Theory and applications to economics : Alfredo Medio, (Cambridge University Press, Cambridge 1992) pp. xv + 344, $54.95," Journal of Economic Behavior & Organization, Elsevier, vol. 26(2), pages 308-310, March.
- Rassenti, Stephen & Reynolds, Stanley S. & Smith, Vernon L. & Szidarovszky, Ferenc, 2000. "Adaptation and convergence of behavior in repeated experimental Cournot games," Journal of Economic Behavior & Organization, Elsevier, vol. 41(2), pages 117-146, February.
- Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521558747, December.
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