 The competition between private information and herding seems the key ingredient to explain some of the main features of financial markets. We are currently developping a mathematical model that exhibits new phase transitions and allows us to understand how agents can use the information of other agents in order to make better forecasts on a future event.
In this figure, the success rate q of the herding strategy is plotted as a function of the probability of herding eta. The personal success rate is p=0.55 when agents follow only their private information. The number of agents being considered when using the herding strategy is K=11. Note the phase transition near eta=0.4 where more and more agents are following the majority. When eta=1, all agents are herding, i.e. no information is entering the system: they act randomly and have a success rate q=0.5. The analytical solution for q is given by the formula: (derivation in référence [1]) | 
