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We examine a price competition game between two intermediaries offering to match two sides of a market on the Internet. Competition is characterized by asymmetric network externalities. We account for some specificities of cybermediation, in particular access versus usage pricing and the possibility of using the services of several intermediaries. When only registration fees are used and agents register with at most one cybermediary, there exists an equilibrium where one firm corners the market with positive profits. Introducing either fees contingent on successful matching or the possibility of registration with two cybermediaries make these profits vanish. Other types of equilibria are discussed.