Content sharing in social networks is now one of the most common activities of internet users. In sharing content, users often have to make access control or privacy decisions that impact other stakeholders or co-owners. These decisions involve negotiation, either implicitly or explicitly. Over time, as users engage in these interactions, their own privacy attitudes evolve, influenced by and consequently influencing their peers. In this paper, we present a variation of the one-shot Ultimatum Game, wherein we model individual users interacting with their peers to make privacy decisions about shared content. We analyze the effects of sharing dynamics on individuals’ privacy preferences over repeated interactions of the game. We theoretically demonstrate conditions under which users’ access decisions eventually converge, and characterize this limit as a function of inherent individual preferences at the start of the game and willingness to concede these preferences over time. We provide simulations highlighting specific insights on global and local influence, short-term interactions and the effects of homophily on consensus.