Information shared through Social Media may affect more than one user’s privacy e.g., Information that depicts different users, comments that mention different users, events in which different users are invited, etc. Many types of privacy management support in present mainstream Social Media foundation makes users unable to appropriately control the sender and receiver. Computational mechanisms that are able to merge the privacy preferences of different users into a single policy for an item can help solve this problem. Merging different user’s personal preferences is difficult hence conflicts occur in privacy preferences, so methods to resolve conflicts are needed. Moreover, these techniques need to consider how users’ would actually reach an engagement about a solution to the conflict in order to propose solutions that can be acceptable by all of the users affected by the information to be shared. present approaches are either too demanding or only consider fixed ways of aggregating privacy preferences. Here, we introduce the basic computational procedure to overcome problems in Social Media that is able to adapt to different situations by modeling the concessions that users make to reach answers to the conflicts. The present results of a user study in which our introduced mechanism outperformed other present approaches in terms of how many times each approach matched users’ action. Computational mechanisms that are able to merge the privacy preferences of multiple users into a single policy for an item can help solve this problem. However, merging multiple users’ privacy preferences is not an easy task, because privacy preferences may conflict, so methods to resolve conflicts are needed. Moreover, these methods need to consider how users’ would actually reach an agreement about a solution to the conflict in order to propose solutions that can be acceptable by all of the users affected by the item to be shared. Current approaches are either too demanding or only consider fixed ways of aggregating privacy preferences. In this project, we propose the first computational mechanism to resolve conflicts for multi-party privacy management in Social Media that is able to adapt to different situations by modeling the concessions that users make to reach a solution to the conflicts. We also present results of a user study in which our proposed mechanism outperformed other existing approaches in terms of how many times each approach matched users’ behavior.