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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2024. "On properties of the set of awards vectors for a claims problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 137-167, April.
    • Handle: RePEc:spr:topjnl:v:32:y:2024:i:1:d:10.1007_s11750-023-00661-9
    DOI: 10.1007/s11750-023-00661-9
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