Informational cascade as a pinning control problem

Informational cascades are imitation phenomena which can emerge in financial markets. When an informational cascade occurs, the agents completely disregard their own information and blindly follow the behavior of the other traders. The models in the literature, although capable of replicating this phenomenon, do not take into account the possibility of reproducing cascades of different intensities, displayed by empirical evidences. To overcome this limitation, we introduce a new model of opinion dynamics capable of replicating informational cascades of different magnitudes. This is accomplished by viewing informational cascades as a diffusion of a certain opinion in a network of financial agents, whose trading strategies dynamically depend on that of their neighbors according to a nonlinear law. Following the logic of pinning control, we model the generic exogenous information triggering informational cascades as a control signal fed by an external entity, the pinner, to a subset of agents. By virtue of the received information, they take the trading action that will be imitated by the non informed traders. In this framework, we can exploit some results of the so called “partial pinning control” to assess the number of non informed agents which reach consensus on the pinner’s opinion, and thus are involved in the informational cascade. This assessment is based on the topological structure connecting the agents: different topologies generate informational cascades of different magnitudes. We test our model of opinion dynamics in an agent-based artificial financial market, showing its capability of replicating informational cascades of different and predictable intensities.