Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players
AbstractA 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.
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Bibliographic InfoArticle provided by CEJEME in its journal Central European Journal of Economic Modelling and Econometrics.
Volume (Year): 2 (2010)
Issue (Month): 2 (March)
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Bertrand duopoly; heterogeneous expectations; nonlinear dynamics; chaos;
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
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