Discrete-space agglomeration model with social interactions: Multiplicity, stability, and continuous limit of equilibria

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Journal of Mathematical Economics, ISSN: 0304-4068, Vol: 69, Page: 22-37

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Takashi Akamatsu, Shota Fujishima, Yuki Takayama
Elsevier BV
Economics, Econometrics and Finance, Mathematics
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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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