Social Power Games in Concatenated Opinion Dynamics

In this paper we propose and solve a social power game, i.e., a strategic game formulated on an opinion dynamics model and in which the agents aim to maximize their social power. As model we consider the concatenated Friedkin-Johnsen (FJ) model, which describes opinion evolution over a sequence of discussion events, while as actions we take the stubbornness coefficients, which can be freely chosen by the agents in order to maximize their social power, here corresponding to the utility function of the game. We show that the optimal solution of the social power game corresponds to an "early mover" strategy, in the sense that being stubborn as much as possible in early meetings allows to achieve the highest social power. This early mover advantage can be explained in terms of a diminishing return law that exists in the concatenated FJ model.