### Abstract

We study an imperfect quantity competition on networks that represent rivalry relationships among firms. We show that the more heterogeneous the underlying network is, the more the output and the price are. The output and the price on scale-free networks are counter-intuitively the same as those in the monopoly regardless of the number of rival firms. We also show that any inverse demand function represented by a network has the corresponding utility function, which justifies the inverse demand function.

Original language | English |
---|---|

Pages (from-to) | 5453-5460 |

Number of pages | 8 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 392 |

Issue number | 21 |

DOIs | |

Publication status | Published - 2013 Nov 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Imperfect competition
- Monopoly solution
- Network heterogeneity
- Scale-free networks

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*392*(21), 5453-5460. https://doi.org/10.1016/j.physa.2013.06.017

**An imperfect competition on scale-free networks.** / Konno, Tomohiko.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 392, no. 21, pp. 5453-5460. https://doi.org/10.1016/j.physa.2013.06.017

}

TY - JOUR

T1 - An imperfect competition on scale-free networks

AU - Konno, Tomohiko

PY - 2013/11/1

Y1 - 2013/11/1

N2 - We study an imperfect quantity competition on networks that represent rivalry relationships among firms. We show that the more heterogeneous the underlying network is, the more the output and the price are. The output and the price on scale-free networks are counter-intuitively the same as those in the monopoly regardless of the number of rival firms. We also show that any inverse demand function represented by a network has the corresponding utility function, which justifies the inverse demand function.

AB - We study an imperfect quantity competition on networks that represent rivalry relationships among firms. We show that the more heterogeneous the underlying network is, the more the output and the price are. The output and the price on scale-free networks are counter-intuitively the same as those in the monopoly regardless of the number of rival firms. We also show that any inverse demand function represented by a network has the corresponding utility function, which justifies the inverse demand function.

KW - Imperfect competition

KW - Monopoly solution

KW - Network heterogeneity

KW - Scale-free networks

UR - http://www.scopus.com/inward/record.url?scp=84882852681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84882852681&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2013.06.017

DO - 10.1016/j.physa.2013.06.017

M3 - Article

AN - SCOPUS:84882852681

VL - 392

SP - 5453

EP - 5460

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 21

ER -