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Perturbed cusp catastrophe in a population game: Spatial economics with locational asymmetries

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  • Kiyohiro Ikeda
  • Yuki Takayama
  • José M. Gaspar
  • Minoru Osawa

Abstract

This paper studies the cusp catastrophe in a two‐strategy population game with exogenous locational asymmetries and its application to spatial economics. We derive approximating games of two kinds: a cusp catastrophe form and a more general form. As a novel contribution of this paper, the effects of an arbitrary number of regional asymmetries are expressed using only three asymmetry parameters, thereby allowing for an analytical analysis. We find a new behavior with hysteresis using the general form. The usefulness of the forms is demonstrated for two economic geography models. A numerical recipe is presented to construct the cusp catastrophe form.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jregsc:v:62:y:2022:i:4:p:961-980
    DOI: 10.1111/jors.12582
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    1. Jos'e M. Gaspar, 2024. "A note on heterogeneity, trade integration and spatial inequality," Papers 2404.09796, arXiv.org.

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