Most likely retail agglomeration patterns: Potential maximization and stochastic stability of spatial equilibria

TL;DR

This paper models retail clustering as a potential maximization problem, showing that global optimization yields unique, stable spatial equilibria and analyzing how shopping costs and attractiveness influence retail agglomeration patterns.

Contribution

It introduces a novel approach using potential maximization from evolutionary game theory to determine stable retail distribution equilibria.

Findings

Global maximization yields unique stable equilibria.

Lower shopping costs reduce retail cluster numbers.

Increased attractiveness of large retail areas promotes agglomeration.

Abstract

We study a model of retail agglomeration where consumers are more likely to visit zones with a higher concentration of shops. This agglomerative effect makes zones with many retailers more attractive. The spatial distribution of retailers in equilibrium is endogenously determined in response to the spatial pattern of shopping demand. In such a setting, multiple locally stable equilibria may arise, and the outcome can depend on the initial distribution of shops. To address this issue, we apply an approach from evolutionary game theory, selecting the equilibrium that maximizes a potential function representing the incentives of retailers. We demonstrate the method in a two-dimensional spatial setting. Compared to local stability based on gradual, myopic adjustments, this global maximization leads to a unique and more robust prediction. As expected, the number of retail clusters decreases either when shopping costs for immobile consumers fall or when the attractiveness of larger retail concentrations increases.