Theory of linear and integer programming
Theory of linear and integer programming
NP-completeness of some problems concerning voting games
International Journal of Game Theory
On the complexity of cooperative solution concepts
Mathematics of Operations Research
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Finding nucleolus of flow game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computational complexity of weighted threshold games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
On the computational complexity of weighted voting games
Annals of Mathematics and Artificial Intelligence
Monotone cooperative games and their threshold versions
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Non-transferable utility coalitional games via mixed-integer linear constraints
Journal of Artificial Intelligence Research
On the complexity of core, kernel, and bargaining set
Artificial Intelligence
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
Computing stable outcomes in hedonic games with voting-based deviations
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
The least-core of threshold network flow games
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Rip-off: playing the cooperative negotiation game
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Concise characteristic function representations in coalitional games based on agent types
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
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Weighted voting games (WVG) are coalitional games in which an agent's contribution to a coalition is given by his weight, and a coalition wins if its total weight meets or exceeds a given quota. These games model decision-making in political bodies as well as collaboration and surplus division in multiagent domains. The computational complexity of various solution concepts for weighted voting games received a lot of attention in recent years. In particular, Elkind et al.(2007) studied the complexity of stability-related solution concepts in WVGs, namely, of the core, the least core, and the nucleolus. While they have completely characterized the algorithmic complexity of the core and the least core, for the nucleolus they have only provided an NP-hardness result. In this paper, we solve an open problem posed by Elkind et al. by showing that the nucleolus of WVGs, and, more generally, k-vector weighted voting games with fixed k, can be computed in pseudopolynomial time, i.e., there exists an algorithm that correctly computes the nucleolus and runs in time polynomial in the number of players n and the maximum weight W. In doing so, we propose a general framework for computing the nucleolus, which may be applicable to a wider of class of games.