Existing online social networks (OSNs) only allow a single user to restrict access to her/his data but cannot provide any mechanism to enforce privacy concerns over data associated with multiple users. This situation leaves privacy conflicts largely unresolved and leads to the potential disclosure of users' sensitive information. To address such an issue, a MultiParty Access Control (MPAC) model was recently proposed, including a systematic approach to identify and resolve privacy conflicts for collaborative data sharing in OSNs. In this paper, we take another step to further study the problem of analyzing the strategic behavior of rational controllers in multiparty access control, where each controller aims to maximize her/his own benefit by adjusting her/his privacy setting in collaborative data sharing in OSNs. We first formulate this problem as a multiparty control game and show the existence of unique Nash Equilibrium (NE) which is critical because at an NE, no controller has any incentive to change her/his privacy setting. We then present algorithms to compute the NE and prove that the system can converge to the NE in only a few iterations. A numerical analysis is also provided for different scenarios that illustrate the interplay of controllers in the multiparty control game. In addition, we conduct user studies of the multiparty control game to explore the gap between game theoretic approaches and real human behaviors.