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The proliferation of the internet technologies and applications has intensified business activities on the Internet. This study considered the price competition between two shopping channels, one on-line seller and the other traditional off-line retailer. Based on the Hotelling’s linear market model, we derive the Nash and Stackelberg equilibria as a function of the cost parameters which represent the characteristics of the online and off-line channels. By analyzing the equilibrium solutions, the following significant findings were obtained. First, pricing by Stackelberg equilibrium always outperformed that of Nash equilibrium. However the value of the cost parameters played a crucial role in determining both channels’ preferred position (price leader or follower). Second, the online seller could benefit more in terms of profit by lowering its efficiency when its efficiency belongs to a certain interval. Third, when the online seller’s efficiency is low, lowering its delivery cost has no contribution to its profit. To benefit more from lowering its delivery cost, increasing its channel efficiency to a certain level should be preceded.