Rationality, Stability, and Endogenous Price Formation in Spatially Interdependent Markets

Spatial competition between firms is standard fare for traditional location theory and contemporary geographical economics. In this paper we examine the implications of modeling spatial competition using an approach grounded in geographical political economy, using mathematics as the language of theory. We make no presumptions about the existence of, or agents' prior knowledge about, equilibrium; utilizing methodologies from nonlinear dynamics appropriate to this situation. For competition between equally spaced retailers along an unbounded linear market, selling a homogeneous commodity to uniformly dispersed consumers we show that Nash equilibrium, which rationalizes the existence and persistence of spatial price equilibria, need not hold. Depending on behavioral parameters, out-of-equilibrium dynamics may not converge toward equilibrium, displaying instead limit-cycle or aperiodic behavior. Further, even for cases that do converge, it can be rational for firms in equilibrium to set prices which depart from it, thereby increasing their profits. The presumptions of geographical economics concerning equilibrium are not adequate to make sense of capitalist spatial price competition.