The dynamics of Bertrand model with bounded rationality

Jixiang Zhang, Qingli Da and Yanhua Wang

Chaos, Solitons & Fractals, 2009, vol. 39, issue 5, 2048-2055

Abstract: 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.

Date: 2009
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Citations: View citations in EconPapers (26)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:39:y:2009:i:5:p:2048-2055

DOI: 10.1016/j.chaos.2007.06.056

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