Convex Cooperative Games
Introduced by Shapley in (Shapley 1971), convex cooperative games capture the intuitive property some games have of "snowballing". Specifically, a game is convex if its characteristic function is supermodular:
It can be shown (see, e.g., Section V.1 of (Driessen 1988)) that the supermodularity of is equivalent to
that is, "the incentives for joining a coalition increase as the coalition grows" (Shapley 1971), leading to the aforementioned snowball effect. For cost games, the inequalities are reversed, so that we say the cost game is convex if the characteristic function is submodular.
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