We consider an incumbent firm and a more efficient entrant, both offering a network good to several asymmetric buyers, and both being able to price discriminate. The good has positive value to buyers only if the network size exceeds a certain threshold. The incumbent's installed base guarantees this critical size to the incumbent, while the entrant needs to attract enough ‘new’ buyers to meet this threshold. We show that price discrimination (in the various forms it may take) reduces the set of achievable socially efficient entry equilibria, and discuss the policy implications of this result.