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Today, Online Social Network (OSN) services have evolved as the highest-growing medium, enabling various online activities on one platform. However, they also bring new threats and privacy issues to the community. In a reliable OSN service, a user should be able to set up his or her desired level of information sharing with a certain group of other users. Unfortunately, there are attackers that may attempt to expose OSN users' private information or conceal the information that the user would like to share with other users. Therefore, in this paper, we propose a game theoretic approach for helping OSN users determine their optimum policy on OSNs in terms of data sharing, based on a two-player (i.e., agent and opponent) zero-sum Markov game model.