We investigate the strategic behavior of firms in a Hotelling spatial setting. The innovation is to combine two important features that are ubiquitous in real markets: (1) the location space is two-dimensional, often with physical restrictions on where firms can locate; (2) consumers with some probability shop at firms other than the nearest. We characterise convergent Nash equilibria (CNE), in which all firms cluster at one point, for several alternative markets. In the benchmark case of a square convex market, we provide a new direct geometric proof of a result by Cox (Am J Political Sci 31:82–108, 1987) that CNE can arise in a sufficiently central part of the market. The convexity of the square space is of restricted realism, however, and we proceed to investigate grids, which more faithfully represent a stylised city’s streets. We characterise CNE, which exhibit several new phenomena. CNE in more central locations tend to be easier to support, echoing the unrestricted square case. However, CNE on the interior of edges differ substantially from CNE at nodes and follow quite surprising patterns. Our results also highlight the role of positive masses of indifferent consumers, which arise naturally in a network setting. In most previous models, in contrast, such masses cannot exist or are assumed away as unrealistic.

我们调查了酒店在Hotelling空间环境中的战略行为。创新之处在于结合了两个在现实市场中无处不在的重要特征：（1）位置空间是二维的，通常对公司的位置有物理限制；（2）有一定可能性的消费者在最近的公司以外的商店购物。我们表征了收敛的纳什均衡（CNE），在该均衡中，所有公司针对多个替代市场集中在一个点上。在方形凸市场的基准案例中，我们提供了Cox结果的新的直接几何证明（Am J政治科学31：82–108，1987），证明CNE可以出现在市场的足够中心部分。正方形空间的凸度是有限的现实主义，但是，我们将继续研究网格，这些网格更忠实地代表了一座程式化城市的街道。我们对CNE进行了表征，它表现出几种新现象。位于中心位置的CNE倾向于更容易支撑，与无限制的方形情况相呼应。但是，边缘内部的CNE与节点处的CNE完全不同，并且遵循非常令人惊讶的模式。我们的研究结果还强调了在网络环境中自然产生的无动于衷的消费者群体的作用。相反，在大多数以前的模型中，这样的质量不存在或被认为是不现实的。这自然是在网络环境中产生的。相反，在大多数以前的模型中，这样的质量不存在或被认为是不现实的。这自然是在网络环境中产生的。相反，在大多数以前的模型中，这样的质量不存在或被认为是不现实的。