A Herding Model with Preferential Attachment and Fragmentation

We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent joins an existing group, or (ii) with probability $1-p$ a group is fragmented into individual agents. The group size distribution is found to be power-law with an exponent that depends continuously on $p$. A number of variants of our basic model are discussed. Comparisons are made between these models and other models of herding and random growing networks.