##
**Study on a 3-dimensional game model with delayed bounded rationality.**
*(English)*
Zbl 1229.91223

Summary: A nonlinear dynamic triopoly game model is studied based on the theory of nonlinear dynamics and previous researches in this paper. A lagged structure is introduced to the model to study stability conditions of the Nash equilibrium under a local adjustment process when players price their products with delayed bounded rationality. Numerical simulations are provided to demonstrate the complexity of system evolvement and influence of the strategy of delayed bounded rationality on system stability. We find that besides the lagged structure, suitable delayed parameters are also important factors to eliminate chaos or expand the stable region of the system, and various players’ adjustment parameters have different effect on stability of the system.

### MSC:

91B55 | Economic dynamics |

91A26 | Rationality and learning in game theory |

91A20 | Multistage and repeated games |

91B24 | Microeconomic theory (price theory and economic markets) |

PDF
BibTeX
XML
Cite

\textit{J. Peng} et al., Appl. Math. Comput. 218, No. 5, 1568--1576 (2011; Zbl 1229.91223)

Full Text:
DOI

### References:

[1] | Kople, Michael, Simple and complex adjustment dynamics in Cournot duopoly models, Chaos, solitons and fractals, 12, 2031-2048, (1996) · Zbl 1080.91541 |

[2] | Ahmed, E.; Agiza, H.N.; Hassan, S.Z., On modifications of puu’s duopoly, Chaos, solitons and fractals, 11, 1025-1028, (2000) · Zbl 0955.91045 |

[3] | Agiza, H.N.; Elsadany, A.A., Nonlinear dynamics in the Cournot duopoly game with heterogeneous players, Physica A, 320, 512-524, (2003) · Zbl 1010.91006 |

[4] | Yassen, M.T.; Agiza, H.N., Analysis of a duopoly game with delayed bounded rationality, Applied mathematics and computation, 138, 387-402, (2003) · Zbl 1102.91021 |

[5] | Ji, Wei-Zhuo; Ma, Jun-Hai, Complexity of repeated game model in electric power duopoly, Journal of systems and management, 3, 251-256, (2007) |

[6] | Chen, Fang; Ma, Jinhai; Chen, Xiaoqiang, The study of dynamic processes of the triopoly games in Chinese 3G telecommunication market, Chaos, solitons and fractals, 42, 1542-1551, (2009) · Zbl 1198.91164 |

[7] | Zhou, Huizhong, Microeconomics, (2003), Shanghai People’s Publishing House Shanghai |

[8] | Glulick, D., Encounters with chaos, (1992), McGraw-Hill New York |

[9] | V. Bohm, J. Wenzelbarger, Cycles and local stability in discrete dynamical systems with delay structure, discussion paper 320, Department of Economics, Bielefeled University, 1996. |

[10] | Junhai, Ma; Jing, Peng; decision, Study of an oligopoly game model with delayed, Journal of systems engineering, 25, 6, 812-817, (2010) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.