Statistical properties of agent-based market area model

TL;DR

This paper introduces a one-dimensional agent-based model of firms with spatial selling areas, analyzing how overlaps and demand feedback influence firm size distribution, revealing conditions under which Pareto's law emerges.

Contribution

It presents a novel spatial agent-based market model incorporating demand feedback and overlaps, elucidating conditions for Pareto distribution emergence.

Findings

Pareto's law holds within specific parameter ranges.

Minimum pair correlation correlates with Pareto distribution.

Overlap-induced negative feedback influences firm size dynamics.

Abstract

One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this representation, the firm size is directly associated with the size of its selling interval. The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Pareto's law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.