论文标题
与单位点功能的空间竞争
Spatial competition with unit-demand functions
论文作者
论文摘要
本文研究了两家公司之间以某些预定的固定价格出售同质商品的公司之间的空间竞争游戏。一群消费者分布在实际线路上，两家公司同时选择在同一空间中的位置。从其中一家公司购买时，消费者会产生固定价格加上一些运输成本，这些成本随着与公司的距离而增加。假设每个消费者都准备好购买公司的一个单位，无论公司的地点如何，公司都会汇聚到中间位置：“差异很小”。在本文中，我们放松了这个假设，并假设消费者准备覆盖的距离有上限。我们表明，该游戏在纯策略中始终具有至少一个NASH平衡。在这个更一般的假设下，“最小分化原理”一般不再存在。在平衡处，公司选择“最小”，“中间”或“完全”的分化，具体取决于消费者准备覆盖的关键距离以及消费者位置分布的形状。
This paper studies a spatial competition game between two firms that sell a homogeneous good at some pre-determined fixed price. A population of consumers is spread out over the real line, and the two firms simultaneously choose location in this same space. When buying from one of the firms, consumers incur the fixed price plus some transportation costs, which are increasing with their distance to the firm. Under the assumption that each consumer is ready to buy one unit of the good whatever the locations of the firms, firms converge to the median location: there is "minimal differentiation". In this article, we relax this assumption and assume that there is an upper limit to the distance a consumer is ready to cover to buy the good. We show that the game always has at least one Nash equilibrium in pure strategy. Under this more general assumption, the "minimal differentiation principle" no longer holds in general. At equilibrium, firms choose "minimal", "intermediate" or "full" differentiation, depending on this critical distance a consumer is ready to cover and on the shape of the distribution of consumers' locations.
