A Heterogeneous Agent Herding Model with Time and Space Effect

We propose a heterogeneous agent herding model, in which the agent clusters are in active or inactive states. When agent clusters are in active states, they tend to buy or sell. In active states, an exchange may occur when two heterogeneous agent clusters encounter each other, and they may merge into a bigger one when two homogeneous agent clusters meet. The ratio of successful exchange or merging depends on two parameters: i.e. the reliability k, reflecting the credible degree in the interacting agent clusters, being the space effect of the market, and the response degree q, reflecting the influence of the former trading to the current action, being the time effect of the market. Our numerical calculation shows that the dynamics of the model exhibits some behaviour very close to real markets when tuning the reliability and the degree of reaction to some specific values.