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

  1. Miguel Ángel Mirás Calvo 1
  2. Iago Núñez Lugilde 2
  3. Carmen Quinteiro Sandoming 3
  4. Estela Sánchez Rodríguez 2
  1. 1 Departamento de Matemáticas, RGEAF. Universidade de Vigo, Vigo, Spain
  2. 2 Departamento de Estatística e Investigación Operativa, CINBIO. Universidade de Vigo. Spain
  3. 3 Departamento de Matemáticas, Universidade de Vigo, Vigo, Spain
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Revista:
Top

ISSN: 1863-8279,  1134-5764

Ano de publicación: 2024

Volume: 32

Número: 1

Páxinas: 137-167

Tipo: Artigo

DOI: 10.1007/S11750-023-00661-9 DIALNET GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Top

Resumo

We study the geometric structure of a particular type of nonempty convex polytopes that are the intersection of an n-rectangle with a hyperplane x1 + ⋯ + xn = E, 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.

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