On the complexity of cooperative solution concepts
Mathematics of Operations Research
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
Cooperative facility location games
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Algorithmic Aspects of the Core of Combinatorial Optimization Games
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Restricted Core Stability of Flow Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Algorithms for core stability, core largeness, exactness, and extendability of flow games
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Let Γ = (N, v) be a cooperative game with the player set N and characteristic function v : 2N → 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 non-empty (and a solution in the core can be found in polynomial time). In this paper, we show that, given an imputation x, it is NP-complete 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 NP-hard.