  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.
