Costly location in Hotelling duopoly

We introduce a cost of location into Hotelling's (1929) spatial duopoly model. We derive the general conditions on the cost-of-location function under which a pure strategy price-location Nash equilibrium exists. With linear transportation cost and a suitably specified cost of location that rises toward the center of the Hotelling line, symmetric equilibrium locations are in the outer quartiles of the line, ensuring the existence of pure strategy equilibrium prices. With quadratic transportation cost and a suitably specified cost of location that falls toward the center of the line, symmetric equilibrium locations range from the center to the end of the line.