Volume 2108 of the series Lecture Notes in Computer Science pp 247256
Membership for Core of LP Games and Other Games
 Qizhi FangAffiliated withDepartment of Applied Mathematics, Qingdao Ocean University
 , Shanfeng ZhuAffiliated withDepartment of Computer Science, City University of Hong Kong
 , Maocheng CaiAffiliated withInstitute of Systems Science, Chinese Academy of Sciences
 , Xiaotie DengAffiliated withDepartment of Computer Science, City University of Hong Kong
Abstract
Let Γ = (N, v) be a cooperative game with the player set N and characteristic function v: 2^{N} → R. An imputation of the game is in the core if no subset of players could gain advantage by splitting from the grand coalition of all players. It is well known that, for the linear production game, and the flow game, the core is always nonempty (and a solution in the core can be found in polynomial time). In this paper, we show that, given an imputation x, it is NPcomplete to decide it is not a member of the core, in both games. The same also holds for Steiner tree game. In addition, for Steiner tree games, we prove that testing the total balacedness is NPhard.
Key words
cooperative game core network flow linear programming Steiner tree NPcompleteness Title
 Membership for Core of LP Games and Other Games
 Book Title
 Computing and Combinatorics
 Book Subtitle
 7th Annual International Conference, COCOON 2001 Guilin, China, August 20–23, 2001 Proceedings
 Pages
 pp 247256
 Copyright
 2001
 DOI
 10.1007/3540446796_27
 Print ISBN
 9783540424949
 Online ISBN
 9783540446798
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2108
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 cooperative game
 core
 network flow
 linear programming
 Steiner tree
 NPcompleteness
 Industry Sectors
 eBook Packages
 Editors

 Jie Wang ^{(4)}
 Editor Affiliations

 4. Department of Computer Science, University of Massachusetts
 Authors

 Qizhi Fang ^{(5)}
 Shanfeng Zhu ^{(6)}
 Maocheng Cai ^{(7)}
 Xiaotie Deng ^{(6)}
 Author Affiliations

 5. Department of Applied Mathematics, Qingdao Ocean University, Qingdao, 266003, P.R., China
 6. Department of Computer Science, City University of Hong Kong, Hong Kong, P.Z., China
 7. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, P.R., China
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