Nonlinear dynamics of a duopoly game with adjusting, heterogeneous players, facing increasing marginal costs

• Autorzy: Tomasz Dubiel-Teleszyński
• Języki publikacji: EN

Abstrakty

A repeated, discrete time, nonlinear Cournot duopoly game with adjusting heterogeneous players, i.e. bounded rational and adaptive, is subject of investigation. The game is modeled by a system of two nonlinear difference equations. The evolution of outputs over time is obtained by iteration of a two dimensional noninvertible map. Existing equilibria and their stability are analyzed. Complex behavior is examined by means of numerical analysis. Dynamics of the region of stability is demonstrated. Period doubling route to chaos is presented. Periodic window is identified. Bifurcations, Lyapunov exponents, parameter basin of periodic cycles are computed. Intermittency and crisis are shown. Strange chaotic attractors are displayed and their fractal dimensions are calculated. Sensitive dependence on initial conditions is tested.(original abstract)

Słowa kluczowe

EN

Rationality; Oligopolies; Consumer

PL

Racjonalność; Oligopole; Konsument

• Czasopismo: Department of Applied Econometrics Working Papers
• Rocznik: 2008
• Numer: nr 4
• Strony: 13

Twórcy

autor

Tomasz Dubiel-Teleszyński

• Warsaw School of Economics, Poland

Bibliografia

• Agiza HN. Explicit stability zones for Cournot games with 3 and 4 competitors. Chaos, Solitons and Fractals 1998; 9; 1955-1966.
• Agiza HN. On the stability, bifurcations, chaos and chaos control of Kopel map. Chaos, Solitons and Fractals 1999; 11;1909-1916.
• Agiza HN, Elsadany AA. Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Applied Mathematics and Computation 2004;149; 843-860.
• Agiza HN, Elsadany AA. Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica A 2003; 320; 512-524.
• Agiza HN, Hegazi AS, Elsadany AA. Complex dynamics and synchronization of duopoly game with bounded rationality. Mathematics and Computers in Simulation 2002; 58; 133-146.
• Agiza HN, Hegazi AS, Elsadany AA. The dynamics of Bowley's model with bounded rationality. Chaos, Solitons and Fractals 2001; 9; 1705-1717.
• Bischi GI, Galletgatti M, Naimzada A. Symmetry-breaking bifurcations and representative firm in dynamic duopoly games. Annals of Operations Research 1999; 89; 253-272.
• Bischi GI, Kopel M. Equilibrium selection in a nonlinear duopoly game with adaptive expectations. Journal of Economic Behavior and Organization 2001; 46; 73-100.
• Bischi GI, Lamantia F. Coexisting attractors and complex basins in discrete-time economics models. In: Lines M. (Ed.), Nonlinear dynamical systems in economics. CISM, Springer- WienNewYork; 2005. p. 187-231.
• Bischi GI, Lamantia F. Nonlinear duopoly games with positive cost externalities due to spillover effects. Chaos, Solitons and Fractals 2002; 13; 805-822.
• Bischi GI, Naimzada A. Global analysis of a dynamic duopoly game with bounded rationality. In: Filar JA, Gaitsgory V, Mizukami K (Eds), Advances in Dynamic Games and Applications, vol. 5, Birkhauser; 2000.
• Bischi GI, Stefanini L, Gardini L. Synchronization, intermittency and critical curves in a duopoly game. Mathematics and Computers in Simulation 1998; 44; 559-585.
• Chian ACL, Borotto FA, Rempel EL, Rogers C. Attractor merging crisis in chaotic business cycles. Chaos, Solitons and Fractals 2005; 24; 869-875.
• Chian ACL, Rempel EL, Rogers C. Complex economic dynamics: chaotic saddle, crisis and intermittency. Chaos, Solitons and Fractals 2006; 29; 1194-1218.
• Chian ACL, Rempel EL, Rogers C. Crisis-induced intermittency in non-linear economic cycles. Applied Economics Letters 2007; 14; 211-218.
• Cournot A. Researches into the Mathematical Principles of the Theory of Wealth. Irwin: Homewood; 1963.
• Dana RA, Montrucchio L. Dynamic complexity in duopoly games. Journal of Economic Theory 1986; 40; 40-56.
• Den Haan WJ. The importance of the number of different agents in a heterogeneous asset-pricing model. Journal of Economic Dynamics and Control 2001; 25; 721-746.
• Diks C, Hommes C, Panchenko V, Van der Weide R. E&F Chaos: a user friendly software package for nonlinear economic dynamics. CeNDEF; 2007. http://www1.fee.uva.nl/cendef/.
• Dixit A. Comparative statics for oligopoly. International Economic Review 1986; 27; 107-122.
• Fischer FM. The stability of the Cournot oligopoly solution: the effect of speeds of adjustment and increasing marginal costs. Review of Economic Studies 1961; 28; 125-135.
• Gandolfo G. Economic dynamics. Springer; 1997.
• Gao Y. Complex dynamics in a two dimensional noninvertible map. Chaos, Solitons and Fractals 2007; doi:10.1016/j.chaos.2007.06.051
• Kaplan JL, Yorke YA. A regime observed in a fluid flow model of Lorenz. Communications in Mathematical Physics 1979; 67; 93-108.
• Kopel M. Simple and complex adjustment dynamics in Cournot duopoly models. Chaos, Solitons and Fractals 1996; 12; 2031-2048.
• Leonard D, Nishimura K. Nonlinear dynamics in the Cournot model without full information. Annals of Operations Research 1999; 89; 165-173.
• Medio A, Gallo G. Chaotic dynamics: theory and applications to economics. Cambridge University Press; 1995.
• Medio A, Lines M. Introductory notes on the dynamics of linear and linearized systems. In: Lines M (Ed.), Nonlinear dynamical systems in economics. CISM, SpringerWienNewYork; 2005. p. 1-26.
• Medio A, Lines M. Nonlinear dynamics. A primer. Cambridge University Press; 2001.
• Nusse HE, Yorke JA. Dynamika. Badania numeryczne. PWN: Warszawa; 1998. http://yorke.umd.edu/dynamics/index.html.
• Onazaki T, Sieg G, Yokoo M. Stability, chaos and multiple attractors: a single agent makes a difference. Journal of Economic Dynamics and Control 2003; 27; 1917-1938.
• Ott E. Chaos w ukladach dynamicznych. WNT: Warszawa;1997.
• Pomeau Y, Manneville P. Intermittent transition to turbulence in dissipative dynamical systems. Communications in Mathematical Physics 1980; 74; 187-197.
• Puu T. Chaos in duopoly pricing. Chaos, Solitons and Fractals 1991; 1; 573-581.
• Puu T. Complex oligopoly dynamics. In: Lines M (Ed.), Nonlinear dynamical systems in economics. CISM, SpringerWienNewYork; 2005. p. 165-186.
• Puu T. The chaotic duopolists revisited. Journal of Economic Behavior and Organization 1998; 37; 385-394.
• Rassenti S, Reynolds SS, Smith VL, Szidarovszky F. Adaptation and convergence of behavior in repeated experimental Cournot games. Journal of Economic Behavior and Organization 2000; 41; 117-146.
• Zhang J, Da Q, Wang Y. Analysis of nonlinear duopoly game with heterogeneo players. Economic Modelling 2007; 24;138-148.