The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity

摘要

In order to quantitatively describe interregional migration, we construct two stochastic agent-based models that consist of a large number of agents relocating to obtain higher utility in a discrete bounded domain. In one model we assume that the utility is defined as an increasing affine function of the density of agents. In the other model we assume that the utility is equal to a concave quadratic function of the density of agents. The purpose of the paper is to obtain estimates for the behavior of the models when the number of agents and the time variable tend to infinity.