Spatial duopoly under uniform delivered pricing when firms avoid turning customers away

This paper analyses a spatial duopoly model where firms produce homogeneous goods and set a uniform delivered price. In contrast with the existing literature, the paper shows that an equilibrium always exists. The crucial assumption in restoring the possibility of equilibrium is that firms cannot ration the supply of the good they produce. The market equilibrium is characterised for two different tie-breaking rules. When consumers buy from the nearest firm in case of equal prices, it is found that any symmetric price pair within a given range is a Nash equilibrium. If demand in each local market is equally split between the two firms charging the same price, there is only one equilibrium price pair, at which both firms make zero profits. Some welfare comparisons between the equilibria under the different tie-breaking rules are also provided.