Spatial Market Equilibria on Networks

Abstract

Within the framework of bilevel facility location models in spatial economic competition, there are several different submodels that one can employ to describe economic competition and determine a market equilibrium among firms on the network. Such economic models include the classic spatial price equilibrium (SPE) model, first introduced by Samuelson (1952), and enhanced for over three decades since then (e.g., Takayama and Judge, 1964) as well as models of oligopolistic competition (e.g., Cournot-Nash). In this chapter, we will review the classic SPE model and the oligopolistic spatial Cournot-Nash model. Additionally, we will review non-extremal versions of these models (i.e., variational inequality formulations) and consider their existence and uniqueness properties.

Some of the material in this chapter is adapted and expanded from Friesz, Miller and Tobin (1988A), from Friesz, Tobin and Miller (1989) and from Miller, Tobin and Friesz (1991).