One reason for the popularity of herding models is that one can generate time-series that have statistical properties similar to those of financial market returns. This feature unfortunately vanishes once the number of agents in such a model is increased. This problem is known as N-dependence.

The hierarchical network model we propose overcomes this effect. We divide the total population of agents into two groups of which the first group forms a fully connected core which undergoes an opinion formation process, similar to the herding model of Kirman. The rest of the population, so-called followers, are each linked to only one of the core agents and have an indirect influence on the opinion formation of the core. This setup is supposed to mimic a hierarchical network in a financial market, where a relatively small number of core-agents are acting on behalf of a much greater number of followers. We assume that if a member of the core of this network changes his opinion about the state of the world, the contagious effects onto other core agents will depend on his weight, measured by the number of his followers.

In this model we analyze the effects of differently distributed followers onto the volatility of the system-wide opinion formation process.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/14789 must be provided.

1. System size and network effects in a probabilistic herding model 
2. On competition and the distribution of profit rates