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Bifurcation Theory of a Racetrack Economy in a Spatial Economy Model

Author

Listed:
  • Kiyohiro Ikeda

    (Tohoku University)

  • Mikihisa Onda

    (Tohoku University)

  • Yuki Takayama

    (Kanazawa University)

Abstract

Racetrack economy is a conventional spatial platform for economic agglomeration in spatial economy models. Studies of this economy up to now have been conducted mostly on 2k cities, for which agglomerations proceed via so-called spatial period doubling bifurcation cascade. This paper aims at the elucidation of agglomeration mechanisms of the racetrack economy in a general setting of an arbitrary number of cities. First, an attention was paid to the existence of invariant solutions that retain their spatial distributions when the transport cost parameter is changed. A complete list of possible invariant solutions, which are inherent for replicator dynamics and are dependent on the number of cities, is presented. Next, group-theoretic bifurcation theory is used to describe bifurcation from the uniform state, thereby presenting an insightful information on spatial agglomerations. Among a plethora of theoretically possible invariant solutions, those which actually become stable for spatial economy models are obtained numerically. Asymptotic agglomeration behavior when the number of cities become very large is studied.

Suggested Citation

  • Kiyohiro Ikeda & Mikihisa Onda & Yuki Takayama, 2019. "Bifurcation Theory of a Racetrack Economy in a Spatial Economy Model," Networks and Spatial Economics, Springer, vol. 19(1), pages 57-82, March.
  • Handle: RePEc:kap:netspa:v:19:y:2019:i:1:d:10.1007_s11067-018-9423-0
    DOI: 10.1007/s11067-018-9423-0
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    Cited by:

    1. Kogure, Yosuke & Ikeda, Kiyohiro, 2022. "Group-theoretic Study of Economic Agglomerations on a Square Lattice," MPRA Paper 112842, University Library of Munich, Germany.
    2. Takayama, Yuki & Ikeda, Kiyohiro & Thisse, Jacques-François, 2020. "Stability and sustainability of urban systems under commuting and transportation costs," Regional Science and Urban Economics, Elsevier, vol. 84(C).
    3. 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).
    4. Kiyohiro Ikeda & Yuki Takayama & José M. Gaspar & Minoru Osawa, 2022. "Perturbed cusp catastrophe in a population game: Spatial economics with locational asymmetries," Journal of Regional Science, Wiley Blackwell, vol. 62(4), pages 961-980, September.
    5. Minoru Tabata & Nobuoki Eshima, 2023. "Approximation of a Continuous Core-periphery Model by Core-periphery Models with a Large Number of Small Regions," Networks and Spatial Economics, Springer, vol. 23(1), pages 223-283, March.
    6. Kensuke Ohtake & Atsushi Yagi, 2022. "Pointwise agglomeration in continuous racetrack model," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(2), pages 211-235, May.
    7. 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.
    8. Douglas Silveira & Izak Silva & Silvinha Vasconcelos & Fernando Perobelli, 2020. "The Brexit game: uncertainty and location decision," Papers in Regional Science, Wiley Blackwell, vol. 99(6), pages 1515-1538, December.

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    More about this item

    Keywords

    Bifurcation; Economic agglomeration; Racetrack economy; Replicator dynamics; Spatial economy model;
    All these keywords.

    JEL classification:

    • 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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