Maximizing social power in multiple independent Friedkin-Johnsen models

This paper investigates the problem of maximizing social power for a group of agents, who participate in multiple meetings described by independent Friedkin-Johnsen models. A strategic game is obtained, in which the action of each agent (or player) is her stubbornness over all the meetings, and the payoff is her social power on average. It is proved that, for all but some strategy profiles on the boundary of the feasible action set, each agent's best response is the solution of a convex optimization problem. Furthermore, even with the non-convexity on boundary profiles, if the underlying networks are given by a fixed complete graph, the game has a unique Nash equilibrium. For this case, the best response of each agent is analytically characterized, and is achieved in finite time by a proposed algorithm.