Statistical properties of agent-based market area model
Department of Theoretical Physics and Astrophysics, Pavol Jo
Department of Theoretical Physics and Astrophysics, Pavol Jozef Safarik University at Kosice
Last modified: October 1, 2007
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.