Order cones: A tool for deriving k-dimensional faces of cones of subfamilies of monotone games

In this paper we introduce the concept of order cone. This concept is inspired by the concept of order polytopes, a well-known object coming from Combinatorics. Similarly to order polytopes, order cones are a special type of polyhedral cones whose geometrical structure depends on the properties of a partially ordered set (brief poset). This allows to study these properties in terms of the subjacent poset, a problem that is usually simpler to solve. From the point of view of applicability, it can be seen that many cones appearing in the literature of monotone TU-games are order cones. Especially, it can be seen that the cones of monotone games with restricted cooperation are order cones, no matter the structure of the set of feasible coalitions

The cone of supermodular games on finite distributive lattices

URL des Documents de travail : https://centredeconomiesorbonne.univ-paris1.fr/documents-de-travail-du-ces/Documents de travail du Centre d'Economie de la Sorbonne 2018.10 - ISSN : 1955-611XIn 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.Dans cet article, nous étudions les fonctions sur-modulaires sur des treillis distributifs finis. En relaxant l'hypothèse que le domaine est l'ensemble des parties, nous nous focalisons sur les propriétés géométriques du cône polyhédral de ces fonctions. Nous généralisons le critère pour les rayons extrêmes et étudions le treillis des faces du cône sur-modulaire. Une description explicite des facettes par les inégalités saturées correspondantes est fournie

The cone of supermodular games on finite distributive lattices

International audienceIn 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