Group Reasoning in Social Environments

While modeling group decision making scenarios, the existence of a central authority is often assumed which is in charge of amalgamating the preferences of a given set of agents with the aim of computing a socially desirable outcome, for instance, maximizing the utilitarian or the egalitarian social welfare. Departing from this classical perspective and inspired by the growing body of literature on opinion formation and diffusion, a setting for group decision making is studied where agents are selfishly interested and where each of them can adopt her own decision without a central coordination, hence possibly disagreeing with the decision taken by some of the other agents. In particular, it is assumed that agents belong to a social environment and that their preferences on the available alternatives can be influenced by the number of “neighbors” agreeing/disagreeing with them. The setting is formalized and studied by modeling agents’ reasoning capabilities in terms of weighted propositional logics and by focusing on Nash-stable solutions as the prototypical solution concept. In particular, a thoroughly computational complexity analysis is conducted on the problem of deciding the existence of such stable outcomes. Moreover, for the classes of environments where stability is always guaranteed, the convergence of Nash dynamics consisting of sequences of best response updates is studied, too.