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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.
    2. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress," ULB Institutional Repository 2013/176002, ULB -- Universite Libre de Bruxelles.
    3. Ikeda, Kiyohiro & Akamatsu, Takashi & Kono, Tatsuhito, 2012. "Spatial period-doubling agglomeration of a core–periphery model with a system of cities," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 754-778.
    4. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742.
    5. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117.
    6. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
    7. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735.
    8. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124.
    9. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics :theory and applications," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
    10. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 565-589, March.
    11. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728.
    12. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131.
    13. Pascal Mossay, 2003. "Increasing Returns And Heterogeneity In A Spatial Economy," Working Papers. Serie AD 2003-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    Cited by:

    1. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.
    2. 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).
    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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