On properties of the set of awards vectors for a claims problem

Miguel Ángel Mirás Calvo, Iago Núñez Lugilde, Carmen Quinteiro Sandomingo and Estela Sánchez-Rodríguez ()
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Miguel Ángel Mirás Calvo: RGEAF. Universidade de Vigo
Iago Núñez Lugilde: CINBIO. Universidade de Vigo. SiDOR
Carmen Quinteiro Sandomingo: Universidade de Vigo
Estela Sánchez-Rodríguez: CINBIO. Universidade de Vigo. SiDOR

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 32, issue 1, No 6, 137-167

Abstract: Abstract We study the geometric structure of a particular type of nonempty convex polytopes that are the intersection of an n-rectangle with a hyperplane $$x_1+\dots +x_n=E$$ x 1 + ⋯ + x n = E , $$E>0$$ E > 0 . This type of polytopes arise naturally when studying, for instance, the set of awards vectors for a claims problem, the core of the game associated with a bankruptcy problem, the core-cover set of a game, or the class of two-bound core games. We explore in detail the geometry of such a polytope and provide explicit expressions to compute its volume and its centroid. In particular, we describe a procedure to compute the average-of-awards rule for a claims problem directly from the parameters of the problem. We show that computing the average-of-awards rule is $$\#$$ # P-complete.

Keywords: Claims problems; Set of awards vectors; Average-of-awards rule; Face games; 91A12; 91A40; 52B11 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11750-023-00661-9

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