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Stability of a spatial model of social interactions

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  • Bragard, Jean
  • Mossay, Pascal

Abstract

We study a spatial model of social interactions. Though the properties of the spatial equilibrium have been largely discussed in the existing literature, the stability of equilibrium remains an unaddressed issue. Our aim is to fill up this gap by introducing dynamics in the model and by determining the stability of equilibrium. First we derive a variational equation useful for the stability analysis. This allows to study the corresponding eigenvalue problem. While odd modes are shown to be always stable, there is a single even mode of which stability depends on the model parameters. Finally various numerical simulations illustrate our theoretical results.

Suggested Citation

  • Bragard, Jean & Mossay, Pascal, 2016. "Stability of a spatial model of social interactions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 140-146.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:140-146
    DOI: 10.1016/j.chaos.2015.11.040
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    References listed on IDEAS

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    1. Mossay, P. & Picard, P.M., 2011. "On spatial equilibria in a social interaction model," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2455-2477.
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    Cited by:

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    3. José M. Gaspar, 2018. "A prospective review on New Economic Geography," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 61(2), pages 237-272, September.

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