|
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
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=v1−v2. 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.
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
Linking options:
https://www.mathnet.ru/eng/mgta89 https://www.mathnet.ru/eng/mgta/v4/i3/p58
|
|