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

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  • Akamatsu, Takashi
  • Fujishima, Shota
  • Takayama, Yuki

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.

Suggested Citation

  • Akamatsu, Takashi & Fujishima, Shota & Takayama, Yuki, 2017. "Discrete-space agglomeration model with social interactions: Multiplicity, stability, and continuous limit of equilibria," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 22-37.
    • Handle: RePEc:eee:mateco:v:69:y:2017:i:c:p:22-37
    DOI: 10.1016/j.jmateco.2016.12.007
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    Cited by:

    1. Osawa, Minoru & Akamatsu, Takashi, 2020. "Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach," Journal of Economic Theory, Elsevier, vol. 187(C).
    2. Takayama, Yuki & Kuwahara, Masao, 2017. "Bottleneck congestion and residential location of heterogeneous commuters," Journal of Urban Economics, Elsevier, vol. 100(C), pages 65-79.
    3. Zhi-Chun Li & De-Ping Yu & André de Palma, 2024. "Bottleneck congestion and urban spatial structure with heterogeneous households: Equilibrium, capacity expansion and congestion tolling," THEMA Working Papers 2024-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    4. Zhi-Chun Li Author-Name : Wen-Jing Liu Author-Name : André de Palma, "undated". "Spatial heterogeneity in vehicle license plate lottery rationing," THEMA Working Papers 2024-11, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Akamatsu, Takashi & Mori, Tomoya & Osawa, Minoru & Takayama, Yuki, 2017. "Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications," MPRA Paper 80689, University Library of Munich, Germany.
    6. Takashi Akamatsu & Tomoya Mori & Minoru Osawa & Yuki Takayama, 2019. "Spatial scale of agglomeration and dispersion: Number, spacing, and the spatial extent of cities," Papers 1912.05113, arXiv.org, revised Aug 2024.
    7. André de Palma & Zhi-Chun Li & De-Ping Yu, 2023. "An analytical model for residential location choices of heterogeneous households in a monocentric city with stochastic bottleneck congestion," THEMA Working Papers 2023-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    8. Osawa, Minoru & Akamatsu, Takashi, 2019. "Emergence of Urban Landscapes: Equilibrium Selection in a Model of Internal Structure of the Cities," MPRA Paper 92395, University Library of Munich, Germany.
    9. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.

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    More about this item

    Keywords

    Social interaction; Agglomeration; Discrete space; Potential game; Stability; Evolutionary game theory;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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