Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
International Journal of Game Theory
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Computing the Banzhaf power index in network flow games
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Power and stability in connectivity games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
The Complexity of Power-Index Comparison
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Graph-based coalitional games: an analysis via characteristics
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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
Crowd IQ: aggregating opinions to boost performance
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Proof systems and transformation games
Annals of Mathematics and Artificial Intelligence
Efficient computation of the shapley value for game-theoretic network centrality
Journal of Artificial Intelligence Research
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Sharing rewards in cooperative connectivity games
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected, unweighted multigraph, where edges are players. We examine the computational complexity of computing the voting power indices of edges in the SCG. It is shown that computing Banzhaf values is #P-complete and computing Shapley-Shubik indices or values is NP-hard for SCGs. Interestingly, Holler indices and Deegan-Packel indices can be computed in polynomial time. Among other results, it is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth. It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices. This answers (positively) an open question of whether computing Shapley-Shubik indices for a simple game represented by the set of minimal winning coalitions is NP-hard.