## Abstract

Aiyoshi and Maki (2009) proposed a Nash equilibrium model applying continuous time replicator dynamics to the analysis of oligopoly markets. This paper considered a game problem under the simultaneous constraints of the allocation of product and market shares. The model assumes that a Nash equilibrium solution can be applied and derived the gradient system dynamics that can attain the Nash equilibrium solution without violating the simplex constraints. Models assumed that a minimum of three firms exist within a market, and that these firms behave to maximize their profits, defined as the difference between sales and cost functions with conjectural variations. Before conducting an empirical analysis based on observations of oligopoly markets in the real world, we have to assess the robustness of the Nash equilibrium model by changing profit and cost function parameters, as well as the initial production values and market shares of the firms. This is necessary in order to assess how well observations in the real world match those forecasts by the model. When the model is fragile, no policy implications could be extracted from the model. The paper considers differences of the converged values in the number of firms included in the model, in the numbers of the commodities included in the model, in the specification of firms' profit and cost functions, and in the initial values for the level of production and market share. The approach facilitates understanding of the robustness of attaining equilibrium in an oligopoly market.

Original language | English |
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Title of host publication | 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation |

Subtitle of host publication | Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings |

Pages | 1100-1106 |

Number of pages | 7 |

Publication status | Published - 2009 Dec 1 |

Event | 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM09 - Cairns, QLD, Australia Duration: 2009 Jul 13 → 2009 Jul 17 |

### Publication series

Name | 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, Proceedings |
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### Other

Other | 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM09 |
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Country/Territory | Australia |

City | Cairns, QLD |

Period | 09/7/13 → 09/7/17 |

## Keywords

- Nash equilibrium
- Oligopoly
- Replicator dynamics

## ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computational Mathematics
- Modelling and Simulation