Eur. Phys. J. B 27, 213-218 (2002)
https://doi.org/10.1140/epjb/e20020146

Herd formation and information transmission in a population: non-universal behaviour

¹ Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK
² Department of Applied Physics, South China University of Technology, Guangzhou 510641, PR China
³ Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
⁴ Department of Physics, University of Oxford, Clarendon Laboratory, Oxford OX1 3PU, UK

Corresponding author: ^a phdzheng@scut.edu.cn

Received: 31 December 2001
Published online: 15 May 2002

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 . 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.