Finite-size effect in the Eguíluz and Zimmermann model of herd formation and information transmission.
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 a<<1/N ln N, 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 -3 by the fluctuation effects from the value of -5/2 in the mean-field theory.
Xie
Yanbo
Y
Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei 230026.
Wang
Bing-Hong
BH
Quan
Hongjun
H
Yang
Weisong
W
Hui
P M
PM
D016000:Cluster Analysis; D007257:Information Theory; D017059:Models, Econometric; D008960:Models, Psychological