Herd Formation and Information Transmission in a Population: Non-universal behaviour

Details Herd Formation and Information Transmission in a Population: Non-universal behaviour Herd Formation and Information Transmission in a Population: Non-universal behaviour

2001-12-31

arxiv.org/abs/cond-mat/0112501v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 3 figures, work presented at the EPS APFA3 conference(London, Dec., 2001)

Scientific paper

10.1140/epjb/e20020146

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 Egu\'{\i}luz 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.

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