The cone of supermodular games on finite distributive lattices
Copyright policy )The cone of supermodular games on finite distributive lattices
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.
finite distributive lattice, Games on graphs (graph-theoretic aspects), core, 91A12, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [SHS.ECO]Humanities and Social Sciences/Economics and Finance, polyhedral cone, submodular function, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Cooperative games, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Games involving graphs, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, coalitional game, supermodular function
finite distributive lattice, Games on graphs (graph-theoretic aspects), core, 91A12, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [SHS.ECO]Humanities and Social Sciences/Economics and Finance, polyhedral cone, submodular function, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Cooperative games, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Games involving graphs, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, coalitional game, supermodular function
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