Emergence of Urban Landscapes: Equilibrium Selection in a Model of Internal Structure of the Cities

This paper addresses a longstanding stability issue of equilibria in a seminal model in spatial economic theory, making use of the potential game approach. The model explains the formation of multiple business centers in cities as an equilibrium outcome under the presence of commuting costs of households and positive production externalities between firms. We fist show that the model can be viewed as a large population (nonatomic) potential game. To elucidate properties of stable spatial equilibria in the model, we select global maximizers of the potential function, which are known to be globally stable under various learning dynamics. We find that the formation of business centers (agglomeration of firms) is possible only when the commuting costs of households are sufficiently low and that the size (number) of business centers increases (decreases) monotonically as communication between firms becomes easier. Our results indicate a new range of applications, i.e., spatial economic models, for the theory of potential games.