Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach

Osawa, Minoru and Akamatsu, Takashi (2019): Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach.

Abstract

Using the theory of potential games, this paper addresses the emergence of polycentric struc- tures in cities, resulting from trade-offs between agglomeration economies and congestion effects. We consider a model that explains the formation of multiple business centers in cities as an equilibrium outcome under the presence of households’ commuting costs and positive technological externalities between firms. We first show that the model is a large-population (non-atomic) potential game. To elucidate properties of stable spatial equilibria in the model, we consider local and global maximizations of the potential function of the model, which are known to correspond to various equilibrium refinement criteria. We find that (i) the formation of business centers (agglomeration of firms) is possible only when households’ commuting costs are sufficiently low and that (ii) the size (number) of business centers increases (decreases) monotonically as communication between firms becomes easier.

• Item Type: MPRA Paper
• Language: English
• Keywords: Agglomeration; multiple equilibria; equilibrium refinement; potential game.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R14 - Land Use Patterns

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