  We study a model of vendors competing to sell a homogeneous product to
customers spread evenly along a circular 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.
