  We introduce a framework for studying the effect of cooperation on the
quality of outcomes in utility games. Our framework is a coalitional analog of
the smoothness framework of non-cooperative games. Coalitional smoothness
implies bounds on the strong price of anarchy, the loss of quality of
coalitionally stable outcomes, as well as bounds on coalitional versions of
coarse correlated equilibria and sink equilibria, which we define as
out-of-equilibrium myopic behavior as determined by a natural coalitional
version of best-response dynamics.
  Our coalitional smoothness framework captures existing results bounding the
strong price of anarchy of network design games. We show that in any monotone
utility-maximization game, if each player's utility is at least his marginal
contribution to the welfare, then the strong price of anarchy is at most 2.
This captures a broad class of games, including games with a very high price of
anarchy. Additionally, we show that in potential games the strong price of
anarchy is close to the price of stability, the quality of the best Nash
equilibrium.
