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

Citation data:

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

Publication Year:
2017
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DOI:
10.1016/j.jmateco.2016.12.007
Author(s):
Takashi Akamatsu, Shota Fujishima, Yuki Takayama
Publisher(s):
Elsevier BV
Tags:
Economics, Econometrics and Finance, Mathematics
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article description
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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