Modeling a Large Number of Agents by Types: Models as Large Random Decomposable Structures

This paper introduces methods, based on decomposable random combinatorial analysis, to model a large number of interacting agents. This paper also discusses a largely ignored possibility in the mainstream economic literature that hitherto unknown types of agents may enter the models at some future time. We apply the notion of holding times, and introduce the results of the one- and two-parameter inductive methods of Ewens, Pitman and Zabell to economic literature. More specifically, we use the notion of exchangeable random partitions of a finite set to produce a simple rule of sucession, that is, the expressions for the probabilties for entries by new or known types, conditional on the observed data. Then Ewens equilibrium distriution for the sizes of clusters is introduced, and its use to examine market behavior is sketched, especially when a few types of agents are dominant. We suggest that the approaches of this paper and the notion of holding times are relevant to agent-based simulations because holding times can be used to randomly select agents that “act” first.