Supermodular set function ($f(S\cup T)+f(S\cap T)\ge f(S)+f(T)$)

A real-valued set function is supermodular if it satisfies the displayed inequality. Its negative is a submodular set function. Equivalently, the gain from adding an element cannot decrease as the set grows. This is the defining property of a convex cooperative game, and makes coalition marginal allocations lie in the core of a cooperative game.