Complementary Online Services in Competitive Markets: Maintaining Profitability in the Presence of Network Effects

Assumption 1-(ii) ensures that an equilibrium in which both firms have positive demand prevails when only one of the firms offers the service (else, one firm would set a price to undercut the other and capture the entire market). Similarly, Assumption 1-(iii) ensures both firms have positive demand when both firms offer the service, and Assumption 1-(iv) ensures both firms have positive demand when both sell only the product. Assumption 1-(i) is necessary for the ranges given in Assumptions 1-(ii) and (iii) to be none empty, and is thus implied by the other two conditions. An identical assumption is set in Li and Chen (2012) (where M = 1 and θ denote the degree of network effects), who state: “If t < θ, the network effects dominate employees’ preferences over product’s stand-alone value and employees will always purchase form one single seller.” As is shown below, given condition (i), all S.O.C are satisfied.