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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2012, Volume 4, Issue 3, Pages 58–85 (Mi mgta89)  

This article is cited in 2 scientific papers (total in 2 papers)

The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets

Sergei L. Pecherskyab

a St. Petersburg Institute for Economics and Mathematics RAS
b European University at St. Petersburg
Full-text PDF (539 kB) Citations (2)
References:
Abstract: We explore the implications of the possibility of decomposition of any TU game v into the difference of two convex games v1 and v2, i.e. v=v1v2. In particular, we prove that the Shapley value of a game v is the difference of the Steiner points of the cores C(v1) and C(v2), and, in particular, for a convex game v the Shapley value is the Steiner point of its core. Some properties of this interpretation are studied. A new definition of the Weber set of a TU game is considered.
Keywords: TU games, convex games, the Shapley value, the Steiner point, differences of the cores.
Document Type: Article
UDC: 519.833.5
BBC: 22.18
Language: Russian
Citation: Sergei L. Pechersky, “The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets”, Mat. Teor. Igr Pril., 4:3 (2012), 58–85
Citation in format AMSBIB
\Bibitem{Pec12}
\by Sergei~L.~Pechersky
\paper The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets
\jour Mat. Teor. Igr Pril.
\yr 2012
\vol 4
\issue 3
\pages 58--85
\mathnet{http://mi.mathnet.ru/mgta89}
Linking options:
  • https://www.mathnet.ru/eng/mgta89
  • https://www.mathnet.ru/eng/mgta/v4/i3/p58
  • This publication is cited in the following 2 articles:
    1. Basili M., Chateauneuf A., “Aggregation of Experts' Opinions and Conditional Consensus Opinion By the Steiner Point”, Int. J. Approx. Reasoning, 123 (2020), 17–25  crossref  mathscinet  zmath  isi  scopus
    2. B. N. Khabibullin, “Helly's theorem and shifts of sets. I”, Ufa Math. J., 6:3 (2014), 95–107  mathnet  crossref  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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