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

Takashi Akamatsu, Shota Fujishima, Yuki Takayama

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)22-37
Number of pages16
JournalJournal of Mathematical Economics
Volume69
DOIs
Publication statusPublished - 2017 Mar 1

Keywords

  • Agglomeration
  • Discrete space
  • Evolutionary game theory
  • Potential game
  • Social interaction
  • Stability

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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