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**Analysis of triopoly game with isoelastic demand function and heterogeneous players.**
*(English)*
Zbl 1233.91181

Summary: We analyze a triopoly game model with fully heterogeneous players when the demand function is isoelastic. The three players were considered to be bounded rational, adaptive, and naïve. Existing equilibrium points and their locally asymptotic stability conditions are studied. Complexity of the dynamical system is examined by means of numerical simulations, such as period cycles, bifurcation diagrams, strange attractors and sensitive, dependence on initial conditions. This paper extends the result of F. Tramontana [“Heterogeneous duopoly with isoelastic demand function”, Econ. Model. 27, No. 1, 350–357 (2010)]
who considered a heterogeneous duopoly with isoelastic demand function. Comparisons with respect to the heterogeneous triopoly model of E. M. Elabbasy, H. N. Agiza and A. A. Elsadany [Comput. Math. Appl. 57, No. 3, 488–499 (2009; Zbl 1165.91324)] assuming linear demand function are performed.

### Citations:

Zbl 1165.91324
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\textit{H.-X. Yao} et al., Discrete Dyn. Nat. Soc. 2012, Article ID 280824, 16 p. (2012; Zbl 1233.91181)

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### References:

[1] | A. Cournot, Recherches sur les Principes Mathématiques de la Théoris des Richesses, Hachette, Paris, Farnce, 1838. · Zbl 0174.51801 |

[2] | R. D. Theocharis, “On the stability of the oligopoly problem,” Review of Economic Studies, vol. 27, pp. 133-134, 1959. |

[3] | T. Puu, “On the stability of Cournot equilibrium when the number of competitors increases,” Journal of Economic Behavior and Organization, vol. 66, no. 3-4, pp. 445-456, 2008. |

[4] | T. Palander, “Konkurrens och marknadsjamvikt vid duopoly och oligopoly,” Ekonomisk Tidskrift, vol. 41, no. 124-145, pp. 222-250, 1939. |

[5] | E. Ahmed and H. N. Agiza, “Dynamics of a cournot game with n-competitors,” Chaos, Solitons and Fractals, vol. 9, no. 9, pp. 1513-1517, 1998. · Zbl 0952.91004 |

[6] | T. Puu, “Chaos in duopoly pricing,” Chaos, Solitons and Fractals, vol. 1, no. 6, pp. 573-581, 1991. · Zbl 0754.90014 |

[7] | M. Kopel, “Simple and complex adjustment dynamics in Cournot duopoly models,” Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2031-2048, 1996. · Zbl 1080.91541 |

[8] | A. A. Elsadany, “Dynamics of a delayed duopoly game with bounded rationality,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1479-1489, 2010. · Zbl 1205.91116 |

[9] | H. N. Agiza and A. A. Elsadany, “Nonlinear dynamics in the Cournot duopoly game with heterogeneous players,” Physica A, vol. 320, pp. 512-524, 2003. · Zbl 1010.91006 |

[10] | H. N. Agiza and A. A. Elsadany, “Chaotic dynamics in nonlinear duopoly game with heterogeneous players,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 843-860, 2004. · Zbl 1064.91027 |

[11] | J. Zhang, Q. Da, and Y. Wang, “Analysis of nonlinear duopoly game with heterogeneous players,” Economic Modelling, vol. 24, no. 1, pp. 138-148, 2007. |

[12] | T. Dubiel-Teleszynski, “Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 296-308, 2011. · Zbl 1221.91037 |

[13] | F. Tramontana, “Heterogeneous duopoly with isoelastic demand function,” Economic Modelling, vol. 27, no. 1, pp. 350-357, 2010. |

[14] | T. Puu, “Complex dynamics with three oligopolists,” Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2075-2081, 1996. |

[15] | H. N. Agiza, “Explicit stability zones for Cournot game with 3 and 4 competitors,” Chaos, Solitons and Fractals, vol. 9, no. 12, pp. 1955-1966, 1998. · Zbl 0952.91003 |

[16] | H. N. Agiza, G. I. Bischi, and M. Kopel, “Multistability in a dynamic Cournot game with three oligopolists,” Mathematics and Computers in Simulation, vol. 51, no. 1-2, pp. 63-90, 1999. |

[17] | A. Agliari, L. Gardini, and T. Puu, “The dynamics of a triopoly Cournot game,” Chaos, Solitons and Fractals, vol. 11, no. 13, pp. 2531-2560, 2000. · Zbl 0998.91035 |

[18] | T. Puu and M. R. Marín, “The dynamics of a triopoly Cournot game when the competitors operate under capacity constraints,” Chaos, Solitons and Fractals, vol. 28, no. 2, pp. 403-413, 2006. · Zbl 1124.91025 |

[19] | E. M. Elabbasy, H. N. Agiza, A. A. Elsadany, and H. El-Metwally, “The dynamics of triopoly game with heterogeneous players,” International Journal of Nonlinear Science, vol. 3, no. 2, pp. 83-90, 2007. · Zbl 1394.91067 |

[20] | E. M. Elabbasy, H. N. Agiza, and A. A. Elsadany, “Analysis of nonlinear triopoly game with heterogeneous players,” Computers and Mathematics with Applications, vol. 57, no. 3, pp. 488-499, 2009. · Zbl 1165.91324 |

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