Analysis of nonlinear triopoly game with heterogeneous players

  • Authors:

  • E. M. Elabbasy;H. N. Agiza;A. A. Elsadany

  • Affiliations:

  • Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;Department of Mathematics, Al-Ijailat Teachers' College, Seventh April University, Azzawia, Libya

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

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.