As an application of the cluster size distribution, this chapter models the behavior of price differences in a share market in which a large number of shares of a holding company are traded.

Agents in the market employ various strategies or trading rules. When we put into the same group or cluster all agents with the same strategy, trading rule, excess demand function, or the like, there typically will be many clusters in the market. For convenience of reference, we identify agents with the rules they employ, and say that agents of the same type form a group or cluster.

Clusters evolve over time as agents enter or exit the market, and also as they switch their decision rules or behavioral patterns in response to changing economic environments, such as changing market sentiments. In modeling markets, it is important to realize that it is impossible to say in advance how many clusters are going to be present in the market at any given time. We can only sample agents, that is, take a snapshot or freeze the time, and sample some numbers of agents and count the number of different strategies being used at that particular time. There can be, in principle, an infintely many potential strategies. For example, random combinations of two basic algorithms in different proportions, say, produce different strategies, because they will have different expected performance and variances or risk characteristics. New decision or trading rules will be invented in the future, and so on.