The cone of supermodular games on finite distributive lattices
Michel Grabisch, Tom\'a\v{s} Kroupa
TL;DR
This paper explores the geometric structure of supermodular functions on finite distributive lattices, generalizing extremality criteria and describing the cone's facets and face lattice.
Contribution
It introduces a generalized extremality criterion and provides an explicit description of the supermodular cone's facets for finite distributive lattices.
Findings
Generalized extremality criterion for supermodular functions.
Explicit description of facets via tight linear inequalities.
Analysis of the face lattice of the supermodular cone.
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 extremality and study the face lattice of the supermodular cone. An explicit description of facets by the corresponding tight linear inequalities is provided.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.