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 happens 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 performed in which the procedure is applied to 200 large size test problems with linear, quadratic, exponential and hyperbolic demand functions.

我们为提供相同类型产品并在交付定价上竞争的公司解决位置价格决策问题。如果企业在需求点设定均衡价格，则该问题可以被视为一个区位博弈，其中纳什均衡（NE）被用作解决方案概念。对于空间上分离的市场，由于需求缺乏弹性，存在一个NE，并且可以通过社会成本最小化来找到它，就像网络和平面位置中发生的那样。然而，由于需求对价格敏感，NE的存在尚未被证明，并且社会最优位置可能不是NE。在本文中，我们表明，当需求对价格敏感时，可以在离散和网络位置找到NE。混合整数线性规划公式在最佳响应过程中实现，允许为各种需求函数找到 NE。