Self-organization exhibited by a stochastic agent-based model of firms seeking higher desirability in business expressed by the market potential

We consider an agent-based model consisting of a finite number of firms that move stochastically within a discrete bounded domain in order to obtain higher business profits. The desirability in business is expressed by a certain exogenous random variable and a linear integral operator called market potential. If the number of firms is extremely large and the domain is very wide, then it is almost impossible to fully investigate the model by only doing numerical simulations. In order to overcome the difficulty, we employ a deterministic continuous model that is derived from the stochastic agent-based model by taking the scaling limit. By making use of the continuous model thus derived, we can fully observe self-organization exhibited by the original agent-based model.