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On Stable Equilibria in Discrete-Space Social Interaction Models

Author

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

Abstract

We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of a potential game. Although the equilibrium population distribution in the continuous space is uniquely given by a symmetric unimodal distribution, we find that such a distribution is not always stable in a discrete space. On the other hand, we also show that any sequence of a discrete-space model's equilibria converges with the continuous-space model's unique equilibrium as the discretization is refined.

Suggested Citation

  • Akamatsu, Takashi & Fujishima, Shota & Takayama, Yuki, 2014. "On Stable Equilibria in Discrete-Space Social Interaction Models," MPRA Paper 55938, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:55938
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    File URL: https://mpra.ub.uni-muenchen.de/65225/16/MPRA_paper_65225.pdf
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    References listed on IDEAS

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    Cited by:

    1. Takayama, Yuki, 2015. "Bottleneck congestion and distribution of work start times: The economics of staggered work hours revisited," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 830-847.
    2. 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.

    More about this item

    Keywords

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

    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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