On the complexity of cooperative solution concepts
Mathematics of Operations Research
An algorithm for finding the nucleolus of assignment games
International Journal of Game Theory
The kernel/nucleolus of a standard tree game
International Journal of Game Theory
Characterization sets for the nucleolus
International Journal of Game Theory
Computing the nucleolus of min-cost spanning tree games is NP-hard
International Journal of Game Theory
Combinatorial optimization games
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Cooperative facility location games
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the computation of the nucleolus of a cooperative game
International Journal of Game Theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Computing the nucleolus of weighted voting games
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Restricted Core Stability of Flow Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On the Core and f-Nucleolus of Flow Games
Mathematics of Operations Research
On the computational complexity of weighted voting games
Annals of Mathematics and Artificial Intelligence
The cooperative game theory foundations of network bargaining games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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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We study the algorithmic issues of finding the nucleolus of a flow game. The flow game is a cooperative game defined on a network D = (V, E; ω). The player set is E and the value of a coalition S ⊆ E is defined as the value of the maximum flow from source to sink in the subnetwork induced by S. We show that the nucleolus of the flow game defined on a simple network (ω(e) = 1 for each e ∈ E) can be computed in polynomial time by a linear program duality approach, settling a twenty-three years old conjecture by Kalai and Zemel. In contrast, we prove that both computation and recognition of the nucleolus are NP-hard for flow games with general capacity.