A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain

Authors:
Minoru Tabata;Nobuoki Eshima
Affiliations:
Department of Applied Mathematics, Faculty of Engineering, Kobe University, Kobe 657-8501, Japan;Department of Statistics, Oita Medical University, Oita 879-5593, Japan
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

In order to describe interregional migration, we construct two models that consist of a large number of agents who relocate stochastically within a bounded discrete domain. Each agent of the models moves in order to obtain higher desirability. One is a model whose agents take only the present behavior of agents into account. The other is a model that contains agents relocating on the basis of a conjecture about the behavior (in the future) of agents. We assume that the agents of the latter model form the conjecture by making use of the model containing themselves. In this sense, we can say that the latter model has self-reference. The purpose of the present paper is to study the asymptotic behavior of these two models.