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In this article we study supermodular functions on finite distributivelattices. Relaxing the assumption that the domain is a powerset of a finiteset, we focus on geometrical properties of the polyhedral cone of suchfunctions. Specifically, we generalize the criterion for extremality and studythe face lattice of the supermodular cone. An explicit description of facets bythe corresponding tight linear inequalities is provided.

The cone of supermodular games on finite distributive lattices