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2010 | 2 | 2 | 95-116

Article title

Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players

Content

Title variants

Languages of publication

EN

Abstracts

EN
A 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.

Year

Volume

2

Issue

2

Pages

95-116

Physical description

Dates

received
2010-08-17
accepted
2011-01-15

Contributors

  • Warsaw School of Economics

References

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-070d9bb0-7a65-4607-ba02-dad1ff9095cb
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