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

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.