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” agree-
ing/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.
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