Dynamic Learning, Herding and Guru Effects in Networks

It has been widely accepted that herding is the consequence of mimetic responses by agents interacting locally on a communication network. In extant models, this communication network linking agents, by and large, has been assumed to be fixed. In this paper we allow it to evolve endogenously by enabling agents to adaptively modify the weights of their links to their neighbours by reinforcing 'good' advisors and breaking away from 'bad' advisors with the latter being replaced randomly from the remaining agents. The resulting network not only allows for herding of agents, but crucially exhibits realistic properties of socio-economic networks that are otherwise difficult to replicate: high clustering, short average path length and a small number of highly connected agents, called 'gurus'. These properties are now well understood to characterize 'small world networks' of Watts and Strogatz (1998).