Viral marketing is a methodology which is based on exploiting a pre-existing social network in order to increase brand awareness or product sales through self-replicating viral processes. An essential computational task towards setting up an effective viral marketing campaign is to estimate social influence. Such estimates are usually done by analyzing user activity data. The data analysis and sharing that is needed to estimate social influence raises important privacy issues that may jeopardize the legal, ethical and societal acceptability of such practice, and in turn, the concrete applicability of viral marketing in the real world. Tassa and Bonchi (EDBT 2014) devised secure multi-party protocols that allow a group of service providers and a social networking platform to jointly compute social influence in a privacy preserving manner. They assumed that the players are semi-honest, i.e., that they follow the protocol correctly, but at the same time they examine their view of the protocol in order to extract information on inputs provided by their peers. In this paper we discuss the case of selfish rational players; such players participate in the protocol and follow it correctly only if it is in their best interest and maximizes their utility. We enhance the protocol of Tassa and Bonchi by incorporating into it mechanisms that incentivize the players to participate in the protocol truthfully.