Group-Theoretic Bifurcation Mechanism of Economic Agglomerations on a Square Lattice

Abstract

We elucidate the mechanism of the self-organization of square agglomeration patterns that are described by spatial economic models on a square lattice with periodic boundary conditions. Focusing on the symmetry of the square lattice, we conduct a group-theoretic analysis and obtain bifurcating patterns from the uniform distribution. Furthermore, for the replicator dynamics, which are widely used in economics, we pay attention to the existence of invariant patterns that are solutions to the governing equation for any value of the bifurcation parameter (the trade freeness for spatial economic models). We advance invariant patterns on the square lattice as candidates of stable equilibria. Using a prototype spatial economic model proposed by Forslid and Ottaviano [2003], we numerically show a tendency that bifurcating solutions arrive at invariant patterns after bifurcation. This tendency is advanced as the underlying mechanism of the progress of economic agglomerations that is to be considered in the study of spatial economic agglomerations.