On the Existence and Computation of Nash Equilibrium in Network Competitive Location Under Delivered Pricing and Price Sensitive Demand

Abstract

We address the location-price decision problem for firms that offer the same type of product and compete on delivered pricing. If firms set equilibrium prices at demand points, the problem can be seen as a location game for which the Nash equilibrium (NE) is used as solution concept. For spatially separated markets, with inelastic demand, there exists a NE and it can be found by social cost minimization, as hap- pens in network and planar location. However, with price sensitive demand, the existence of a NE has not been proven yet and socially optimal locations may not be a NE. In this paper we show that a NE can be found in discrete and network location when demand is price sensitive. A Mixed Integer Linear Programming formulation is implemented in the best response procedure which allow to find a NE for a variety of demand functions. An empirical study with data of Spanish municipalities is per- formed in which the procedure is applied to 200 large size test problems with linear, quadratic, exponential and hyperbolic demand functions.