Vertical Differentiation and the Principle of Minimum Horizontal Differentiation in Hotelling's Model

Supposed there is a certain of vertical differentiation between the duopoly in Hotelling's model,we have reached a SPNE in location-price game.As the existence of the vertical differentiation have increased the market power of the firms,and then weakened the firm's motivation of differentiation in the horizontal differentiation product space,we concluded that,in equilibrium,the duopoly's strategy in the horizontal differentiation space is consistent with the principle of minimum differentiation,which is apparently distinguished from the conclusion of all of the presented articles.