Chicken and Egg: Competing Matchmakers

We examine a Bertrand competition game between two intermediaries offering matching services between two sides of a market. Indirect network externalities arise as the probability of finding one's match with a given intermediary increase with the number of agents of the other side who use the services of this intermediary. We formalise some specificities of intermediation on the Internet by allowing registration and transaction prices, and multiple registration. When only registration fees are used and agents register to at most one cybermediary, there exists an equilibrium where one firm corners the market with positive profits, as well as zero profit equilibria where the firms share the market. Introducing either fees that are contingent on successful matching or the possibility of registration with two intermediaries drastically reduces the profits of a dominant firm. Moreover, with multiple registration, new types of positive-profit equilibria emerge where both matchmakers are active and one side of the market registers with both cybermediaries.