Supermodular set function
= Supermodular set function
{title2=$f(S\cup T)+f(S\cap T)\ge f(S)+f(T)$}
= Supermodular
{synonym}
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>.