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

  • D.F. Zheng
  • P.M. Hui
  • K.F. Yip
  • N.F. Johnson

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 Eguıluz 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.

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

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Copyright information

© EDP Sciences, Springer-Verlag 2002

Authors and Affiliations

  • D.F. Zheng
    • 1
  • P.M. Hui
    • 2
  • K.F. Yip
    • 2
  • N.F. Johnson
    • 3
  1. 1.Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UKGB
  2. 2.Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong KongHK
  3. 3.Department of Physics, University of Oxford, Clarendon Laboratory, Oxford OX1 3PU, UKGB

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