基于单位需求函数的空间竞争
Spatial competition with unit-demand functions
摘要：
本文研究了两个厂商以预定的固定价格销售同质商品的空间竞争博弈。消费者群体分布在实际生产线上，两家公司同时选择在同一空间中的位置。当消费者从其中一家公司购买时，消费者承担了固定价格加上一些运输成本，这些成本随着他们到公司的距离而增加。假设每个消费者都愿意购买一个单位的好，无论企业的位置，企业收敛到中间位置：有“最小的差异”。在本文中，我们放松了这一假设，并假设消费者准备购买商品的距离有一个上极限。我们证明了在纯策略下博弈总是至少有一个纳什均衡。在这种更一般的假设下，“最小差别原则”一般不再成立。在均衡状态下，企业选择“最小”、“中间”或“完全”差异化，这取决于消费者准备覆盖的临界距离和消费者位置分布的形状。
英文摘要：
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.
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