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Discrete-Space Agglomeration Model with Social Interactions: Multiplicity, Stability, and Continuous Limit of Equilibria

Akamatsu, Takashi and Fujishima, Shota and Takayama, Yuki (2016): Discrete-Space Agglomeration Model with Social Interactions: Multiplicity, Stability, and Continuous Limit of Equilibria.

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Abstract

This study examines the properties of equilibrium, including the stability, of discrete-space agglomeration models with social interactions. The findings reveal that while the corresponding continuous-space model has a unique equilibrium, the equilibrium in discrete space can be non-unique for any finite degree of discretization by characterizing the discrete-space model as a potential game. Furthermore, it indicates that despite the above result, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined.

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