The literature on game-theoretic models of opinion dynamics in social networks mainly focuses on the Nash equilibrium, which reflects a competitive situation between influencing agents called players. In some real-world situations, however, players negotiate over a game; thus, a different type of solution needs to be considered to account for possible outcomes. In this paper, we examine an opinion dynamics game based on the Friedkin–Johnsen model for which we characterize the Pareto frontier, including the Nash bargaining solution. Next, we analyze this solution when there are changes in the susceptibility of noninfluencing agents with respect to their initial opinions. We also quantify how the Nash equilibrium outcome differs from the outcome prescribed by the Nash bargaining solution.