  Cooperative games provide a framework to study cooperation among
self-interested agents. They offer a number of solution concepts describing how
the outcome of the cooperation should be shared among the players.
Unfortunately, computational problems associated with many of these solution
concepts tend to be intractable---NP-hard or worse. In this paper, we
incorporate complexity measures recently proposed by Feige and Izsak (2013),
called dependency degree and supermodular degree, into the complexity analysis
of cooperative games. We show that many computational problems for cooperative
games become tractable for games whose dependency degree or supermodular degree
are bounded. In particular, we prove that simple games admit efficient
algorithms for various solution concepts when the supermodular degree is small;
further, we show that computing the Shapley value is always in FPT with respect
to the dependency degree. Finally, we note that, while determining the
dependency among players is computationally hard, there are efficient
algorithms for special classes of games.
