The lack of multi-party privacy management support in current mainstream Social Media infrastructures makes users unable to appropriately control to whom co-owned items are shared. Computational mechanisms that are able to merge the privacy preferences of multiple users into a single policy for these kind of items can help solve this problem. As privacy preferences may conflict, these mechanisms need to consider how users' would actually reach an agreement in order to propose acceptable solutions to the conflicts. We propose the first computational mechanism to resolve conflicts for multi-party privacy management in Social Media that adapts to different situations that may motivate different users' concessions and agreements.