The dynamics of Bertrand model with bounded rationality. (English) Zbl 1197.91142

Summary: The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


91B54 Special types of economic markets (including Cournot, Bertrand)
37N40 Dynamical systems in optimization and economics
91B62 Economic growth models
37A99 Ergodic theory
91A26 Rationality and learning in game theory
Full Text: DOI


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