Nonlinear dynamics of a duopoly game with adjusting, heterogeneous players, facing increasing marginal costs
AbstractA 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.
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Bibliographic InfoPaper provided by Department of Applied Econometrics, Warsaw School of Economics in its series Working Papers with number 26.
Length: 13 pages
Date of creation: 25 Mar 2008
Date of revision:
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Cournot duopoly; Bounded rationality; Adaptive expectations; Quadratic cost functions; Chaotic dynamics;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-04-15 (All new papers)
- NEP-BAN-2008-04-15 (Banking)
- NEP-MAC-2008-04-15 (Macroeconomics)
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