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@article{60191,
author = {Bartl, David and Pintér, Miklós},
article_number = {1-3},
doi = {http://dx.doi.org/10.1007/s10479-023-05713-8},
keywords = {TU games with infinitely many players; Bondareva–Shapley Theorem; κ-Core; κ-Balancedness; κ-Additive set function; Duality theorem for infinite LPs},
language = {eng},
issn = {0254-5330},
journal = {Annals of Operations Research},
title = {The κ-core and the κ-balancedness of TU games},
url = {https://link.springer.com/article/10.1007/s10479-023-05713-8},
volume = {332},
year = {2024}
}
TY - JOUR
ID - 60191
AU - Bartl, David - Pintér, Miklós
PY - 2024
TI - The κ-core and the κ-balancedness of TU games
JF - Annals of Operations Research
VL - 332
IS - 1-3
SP - 689-703
EP - 689-703
SN - 0254-5330
KW - TU games with infinitely many players
KW - Bondareva–Shapley Theorem
KW - κ-Core
KW - κ-Balancedness
KW - κ-Additive set function
KW - Duality theorem for infinite LPs
UR - https://link.springer.com/article/10.1007/s10479-023-05713-8
N2 - We consider transferable utility cooperative games with infinitely many players. In particular, we generalize the notions of core and balancedness, and also the Bondareva–Shapley Theorem for infinite TU games with and without restricted cooperation, to the cases where the core consists of κ-additive set functions. Our generalized Bondareva–Shapley Theorem extends previous results by Bondareva (Problemy Kibernetiki 10:119–139, 1963), Shapley (Naval Res Logist Q 14:453–460, 1967), Schmeidler (On balanced games with infinitely many players, The Hebrew University, Jerusalem, 1967), Faigle (Zeitschrift für Oper Res 33(6):405–422, 1989), Kannai (J Math Anal Appl 27:227–240, 1969; The core and balancedness, handbook of game theory with economic applications, North-Holland, 1992), Pintér (Linear Algebra Appl 434(3):688–693, 2011) and Bartl and Pintér (Oper Res Lett 51(2):153–158, 2023).
ER -
BARTL, David and Miklós PINTÉR. The κ-core and the κ-balancedness of TU games. \textit{Annals of Operations Research}. 2024, vol.~332, 1-3, p.~689-703. ISSN~0254-5330. Available from: https://dx.doi.org/10.1007/s10479-023-05713-8.
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