We consider coalitional games played on social networks (graphs), where feasible coalitions are associated with connected subsets of agents. We characterize families of graphs that have polynomially many feasible coalitions, and show that the complexity of computing common solution concepts and parameters of coalitional games on social networks is polynomial in the number of feasible coalitions. Also, we establish a connection between coalitional games on social networks and the synergy coalition group representation, and provide new complexity results for this representation. In particular, we identify a variant of this representation where computing the cost of stability is easy, but computing the value of the least core is hard.
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