The cone of supermodular games on finite distributive lattices

Abstract : In this article, we study supermodular functions on finite distributive lattices. Relaxing the assumption that the domain is a powerset of a finite set, we focus on geometrical properties of the polyhedral cone of such functions. Specifically, we generalize the criterion for extremal rays and study the face lattice of the supermodular cone. An explicit description of facets by the corresponding tight linear inequalities is provided.
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Michel Grabisch, Tomáš Kroupa. The cone of supermodular games on finite distributive lattices. 2018. ⟨halshs-01821712⟩

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