Abstract
In open models of systems with several types of agents, new types of agents that are unexpected or unanticipated may enter at some future time. This possibility is largely ignored in the mainstream economic literature. This paper introduces the results of the two-parameter inductive methods of Ewens, Pitman and Zabell to deal with this problem. These methods postulte entries by unknown types of agents, goods, behavioral rules, or strategies into the model, conditional on the observed data. Ewens one-parameter distribution has been introduced in Aoki (2000c). In economic applications we impose the notion of exchangeable random partitions of a finite set. This produces simple rule of sucession, that is, the expressions for probabilties for entries by new or known types, conditional on the observed data. Using the notion of exchangeable random partitions of a set of finite number of agents, we specify the continous-time Markov chains as economic models with transition rates to reflect the above constraints.
In addition to the usual state vector which lists the number of agents by types, we explain the use of partition vector as state vector in models composed of a large number of exchangeable agents of possibly many types. We illustrate the use of this new state vector by describing the equilibrium distribution of agents by types in partition vector form. We suggest that this approach is also useful in agent-based simulations once we use the notion of holding times to randomly select agents that "acts" first.
