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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, 2016. "Discrete-Space Agglomeration Model with Social Interactions: Multiplicity, Stability, and Continuous Limit of Equilibria," MPRA Paper 74713, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:74713
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    References listed on IDEAS

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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. 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.
    4. Takashi Akamatsu & Tomoya Mori & Minoru Osawa & Yuki Takayama, 2019. "Multimodal agglomeration in economic geography," Papers 1912.05113, arXiv.org, revised Apr 2023.
    5. 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.
    6. 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.
    7. 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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