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We study a model of vendors competing to sell a homogeneous product tocustomers spread evenly along a circular city. This model is based onHotelling's celebrated paper in 1929. Our aim in this paper is to present anecessary and sufficient condition for the equilibrium. This yields arepresentation for the equilibrium. To achieve this, we first formulate themodel mathematically. Next, we prove that the condition holds if and only ifvendors are equilibrium.

Necessary and sufficient condition for equilibrium of the Hotelling model on a circle