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Spatial competition with unit-demand functions

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Document pages: 21 pages

Abstract: This paper studies a spatial competition game between two firms that sell ahomogeneous good at some pre-determined fixed price. A population of consumersis spread out over the real line, and the two firms simultaneously chooselocation in this same space. When buying from one of the firms, consumers incurthe fixed price plus some transportation costs, which are increasing with theirdistance to the firm. Under the assumption that each consumer is ready to buyone unit of the good whatever the locations of the firms, firms converge to themedian location: there is "minimal differentiation ". In this article, we relaxthis assumption and assume that there is an upper limit to the distance aconsumer is ready to cover to buy the good. We show that the game always has atleast one Nash equilibrium in pure strategy. Under this more generalassumption, 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 tocover and on the shape of the distribution of consumers locations.

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