The principle of minimum differentiation revisited

Hotelling's model of differentiated products is examined and modified so that consumers have relatively low reservation prices for the differentiated products. The problem of existence of a Nash equilibrium in prices in a duopoly with given products is analysed. When the reservation price is relatively low, a Nash equilibrium in prices exists for a larger range of products than when the reservation price is infinite. Next I examine product competition with instantaneous adjustment to the Nash equilibrium prices of the previous game. Firms competing in a Nash fashion have tendencies to move away from each other and try to achieve ‘local monopolistic’ positions. This is in sharp contrast with the acclaimed ‘Principle of Minimum Differentiation’ of the original model of Hotelling (of high reservation price) where firms clustered in the product space.