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

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Miranda Menéndez, Pedro and García Segador, Pedro (2020) Order cones: A tool for deriving k-dimensional faces of cones of subfamilies of monotone games. Annals of operations research, 295 . pp. 117-137. ISSN 1572-9338

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Official URL: https://link.springer.com/article/10.1007/s10479-020-03712-7




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Politopos; Análisis combinatorio
Palabras clave (otros idiomas):Monotone games; restricted cooperation; order polytope; cone.
Subjects:Sciences > Mathematics
Sciences > Mathematics > Applied statistics
Sciences > Mathematics > Operations research
ID Code:63213
Deposited On:27 Nov 2020 12:27
Last Modified:30 Nov 2020 08:39

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