  We study a model of vendors competing to sell a homogeneous product to
customers spread evenly along a linear city. This model is based on Hotelling's
celebrated paper in 1929. Our aim in this paper is to present a necessary and
sufficient condition for the equilibrium. This yields a representation for the
equilibrium. To achieve this, we first formulate the model mathematically.
Next, we prove that the condition holds if and only if vendors are equilibrium.
