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

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. [ABSTRACT FROM AUTHOR]