Competition in the presence of social networks: How many service providers maximize welfare?

Competition for clients among service providers is a classical situation discussed in the economics literature. While better service attracts more clients, in some cases clients may prefer to keep using a low quality service if their friends are also using the same service-a phenomenon largely encouraged by the Internet and online social networks. This is evident, for example, in competition between cloud storage service providers such as DropBox, Microsoft SkyDrive and Google Drive. In such settings, the utility of a client depends on both the proposed service level and the number of friends or colleagues using the same service. We study how the welfare of the clients is affected by competition in the presence of social connections. Quite expectantly, competition among two firms can significantly increase the clients' social welfare in comparison with the monopoly case. However, we show that a further increase in competition triggered by the entry of additional firms may be hazardous for the society (i.e., to the clients), which stands in contrast to the typical situation in competition. Indeed, we show via equilibrium analysis that the social benefit of additional firms beyond the duopoly is limited, whereas the potential loss from such an addition is unbounded.