Locational Heterogeneity and Catastrophe in Two-Place Economy

As an independent topic on direct bifurcation, this chapter presents an imperfect pitchfork bifurcation in a two-strategy population game (two-place economy) and its application to an economic geography model by Pflüger (Reg Sci Urban Econ 34(5):565–573, 2004). We derive two types of approximating games: a cusp catastrophe form and a general catastrophe form, considering universal unfolding. The effects of an arbitrary number of regional asymmetries are expressed using only three asymmetry parameters, thereby allowing for theoretical analysis. We propose behavior with hysteresis for the general form and demonstrate its usefulness in the economic geography model with exogenous locational asymmetries. A numerical recipe to construct a cusp catastrophe form, applicable to general economic geography models, is presented.