Finite-size effect in the Eguíluz and Zimmermann model of herd formation and information transmission

Yanbo Xie, Bing Hong Wang, Hongjun Quan, Weisong Yang, P. M. Hui

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14 Scopus citations

Abstract

The Eguíluz and Zimmermann model of information transmission and herd formation in a financial market is studied analytically. Starting from a formal description on the rate of change of the system from one partition of agents in the system to another, a mean-field theory is systematically developed. The validity of the mean-field theory is carefully studied against fluctuations. When the number of agents N is sufficiently large and the probability of making a transaction [formula presented] finite-size effect is found to be significant. In this case, the system has a large probability of becoming a single cluster containing all the agents. For small clusters of agents, the cluster size distribution still obeys a power law but with a much reduced magnitude. The exponent is found to be modified to the value of [formula presented] by the fluctuation effects from the value of [formula presented] in the mean-field theory.

Original languageEnglish
Pages (from-to)6
Number of pages1
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number4
DOIs
StatePublished - 2002
Externally publishedYes

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