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Analysis of nonlinear triopoly game with heterogeneous players. (English) Zbl 1165.91324

Summary: A nonlinear triopoly game with heterogeneous players is presented. We consider three types of players; boundedly rational, adaptive, and naive. A triopoly game is modelled by a three dimensional discrete dynamical system. The stability conditions of the equilibrium points are analyzed. Numerical simulations are used to show bifurcation diagrams, phase portraits, sensitive dependence on initial conditions and fractal dimension. The chaotic behavior of the model has been stabilized on the Nash equilibrium point, by the use of the Pyragas delay feedback control method.

MSC:

91A23 Differential games (aspects of game theory)
37N99 Applications of dynamical systems
93C95 Application models in control theory
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