Opinion formation games with dynamic social influences

We investigate opinion formation games with dynamic social influences, where opinion formation and social relationships co-evolve in a cross-influencing manner. We show that these games always admit an ordinal potential, and so, pure Nash equilibria, and we design a polynomial time algorithm for computing the set of all pure Nash equilibria and the set of all social optima of a given game. We also derive non-tight upper and lower bounds on the price of anarchy and stability which only depend on the players' stubbornness, that is, on the scaling factor used to counterbalance the cost that a player incurs for disagreeing with the society and the cost she incurs for breaking away from her innate beliefs.