On Hotelling's Location Game and the Price Strategy

In this paper, we consider the pure strategy Nash equilibria of generalized Hotelling’s location game model and the condition under which such equilibria actually exists. It is assumed that only locational strategy is taken by two firms in original Hotelling’s game. Such assumption is sometimes efficient especially in the fundamental case study, and the results obtained there are also actually valid in some cases. But, If both price strategy and location strategy are simultaneously adopted, Hotelling’s results are invalid. d’Aspremont, Claude, Gabszewicz & Thisse[1] pointed out that no pure strategy Nash equiliblia exists, using two strategy game models. In this paper, we will consider and reexamine these models and find that the results obtained in Hotelling [2] is not completely invalid