### Abstract

We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Eguíluz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)]. The EZ model, which is a dynamical version of the herd formation model of Cont and Bouchaud (CB), gives a reasonable model for the formation of clusters of agents and for actions taken by clusters of agents. Both the EZ and CB models give a cluster size distribution characterized by a power law with an exponent -5/2. By introducing a size-dependent probability for dissociation of a cluster of agents, we show that the exponent characterizing the cluster size distribution becomes model-dependent and non-universal, with an exponential cutoff for large cluster sizes. The actions taken by the clusters of agents generate the price returns, the distribution of which is also characterized by a model-dependent exponent. When a size-dependent transaction rate is introduced instead of a size-dependent dissociation rate, it is found that the distribution of price returns is characterized by a model-dependent exponent while the exponent for the cluster-size distribution remains unchanged. The resulting systems provide simplified models of a financial market and yield power law behaviour with an easily tunable exponent.

Original language | English (US) |
---|---|

Pages (from-to) | 213-218 |

Number of pages | 6 |

Journal | European Physical Journal B |

Volume | 27 |

Issue number | 2 |

State | Published - May 2 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- 02.50.Le Decision theory and game theory 05.45.Tp Time series analysis
- 05.65.+b Self-organized systems
- 87.23.Ge Dynamics of social systems

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*European Physical Journal B*,

*27*(2), 213-218.

**Herd formation and information transmission in a population : Non-universal behaviour.** / Zheng, D. F.; Hui, P. M.; Yip, K. F.; Johnson, Neil F.

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 27, no. 2, pp. 213-218.

}

TY - JOUR

T1 - Herd formation and information transmission in a population

T2 - Non-universal behaviour

AU - Zheng, D. F.

AU - Hui, P. M.

AU - Yip, K. F.

AU - Johnson, Neil F

PY - 2002/5/2

Y1 - 2002/5/2

N2 - We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Eguíluz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)]. The EZ model, which is a dynamical version of the herd formation model of Cont and Bouchaud (CB), gives a reasonable model for the formation of clusters of agents and for actions taken by clusters of agents. Both the EZ and CB models give a cluster size distribution characterized by a power law with an exponent -5/2. By introducing a size-dependent probability for dissociation of a cluster of agents, we show that the exponent characterizing the cluster size distribution becomes model-dependent and non-universal, with an exponential cutoff for large cluster sizes. The actions taken by the clusters of agents generate the price returns, the distribution of which is also characterized by a model-dependent exponent. When a size-dependent transaction rate is introduced instead of a size-dependent dissociation rate, it is found that the distribution of price returns is characterized by a model-dependent exponent while the exponent for the cluster-size distribution remains unchanged. The resulting systems provide simplified models of a financial market and yield power law behaviour with an easily tunable exponent.

AB - We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population based on the recent model proposed by Eguíluz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)]. The EZ model, which is a dynamical version of the herd formation model of Cont and Bouchaud (CB), gives a reasonable model for the formation of clusters of agents and for actions taken by clusters of agents. Both the EZ and CB models give a cluster size distribution characterized by a power law with an exponent -5/2. By introducing a size-dependent probability for dissociation of a cluster of agents, we show that the exponent characterizing the cluster size distribution becomes model-dependent and non-universal, with an exponential cutoff for large cluster sizes. The actions taken by the clusters of agents generate the price returns, the distribution of which is also characterized by a model-dependent exponent. When a size-dependent transaction rate is introduced instead of a size-dependent dissociation rate, it is found that the distribution of price returns is characterized by a model-dependent exponent while the exponent for the cluster-size distribution remains unchanged. The resulting systems provide simplified models of a financial market and yield power law behaviour with an easily tunable exponent.

KW - 02.50.Le Decision theory and game theory 05.45.Tp Time series analysis

KW - 05.65.+b Self-organized systems

KW - 87.23.Ge Dynamics of social systems

UR - http://www.scopus.com/inward/record.url?scp=0041806497&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041806497&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041806497

VL - 27

SP - 213

EP - 218

JO - European Physical Journal B

JF - European Physical Journal B

SN - 1434-6028

IS - 2

ER -