In the social media era, the ever-increasing utility of Online Social Networks (OSN) services provide a variety of benefits to users, organizations, and service providers. However, OSN services also introduce new threats and privacy issues regarding the data they are dealing with. For instance, in a reliable OSN service, a user should be able to set up his desired level of information sharing and securely manage sensitive data. Currently, few approaches exist that can model OSNs for the purpose, let alone model the effects that attackers can have on these networks. In this work a novel OSN modeling approach is presented to fill the gap. This model is based on an innovative game theoretical approach and it is analyzed both from a theoretical and simulation-oriented view. The game theoretic model is implemented in order to analyze several attack scenarios. As the results show, there are several scenarios where OSN services are very vulnerable and hence more protection mechanisms should be provided in order to secure the data contained across these networks.