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This paper studies Stackelberg price competition in a multi-sided market. The second-mover can engage in divide-and-conquer strategies, which involve cross-subsidies between sides. The paper recovers bounds on profits, and refines the results with a selection criteria whereby consumers resolve coordination failure in favor of a focal platform. It then analyzes perfect price discrimination with network effects, and two-sided market, sheding lights on inefficiencies and strategic choices by platforms. A leading platform may refrain from selling to some side in order to soften competition, it tends to favor excessively balanced market shares and may prefer compatibility to reduce price competition. (JEL D43, D85)