Versioning and advertising in social networks: uniform distributions of valuations

This note studies second-degree discrimination by a platform that sells a two-version (online) service to consumers engaged in a social network. Consumers choose between a premium version, which enhances network externalities, or a free version, which includes advertising about some other product. Under the assumptions that the consumers' valuations for the advertised product are uniformly distributed and that advertising has a signaling structure, we relate optimal pricing to the underlying degree distribution and the hazard rate of the random network. We derive close form expressions for the platform's profits in most prominent real-world social networks where online platforms operate. Platforms that operate in large and relatively sparse networks wish to provide only the free version, whereas platforms serving more densely connected networks prefer to provide both versions.