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.