Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On some central problems in computational complexity.
On some central problems in computational complexity.
Complexity Theory and Cryptology
Complexity Theory and Cryptology
Computing the Banzhaf power index in network flow games
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Divide and conquer: false-name manipulations in weighted voting games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Note: The complexity of power-index comparison
Theoretical Computer Science
Power in threshold network flow games
Autonomous Agents and Multi-Agent Systems
False name manipulations in weighted voting games: splitting, merging and annexation
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Bribery in path-disruption games
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
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The Banzhaf power index is a prominent measure of a player's influence for coalition formation in weighted voting games, an important class of simple coalitional games that are fully expressive but compactly representable. For the normalized Banzhaf index, Aziz and Paterson [1] show that it is NP-hard to decide whether merging any coalition of players is beneficial, and that in unanimity games, merging is always disadvantageous, whereas splitting is always advantageous. We show that for the probabilistic Banzhaf index (which is considered more natural than the normalized Banzhaf index), the merging problem is in P for coalitions of size two, and is NP-hard for coalitions of size at least three. We also prove a corresponding result for the splitting problem. In unanimity games and for the probabilistic Banzhaf index (in strong contrast with the results for the normalized Banzhaf index), we show that splitting is always disadvantageous or neutral, whereas merging is neutral for size-two coalitions, yet advantageous for coalitions of size at least three. In addition, we study the merging and splitting problems for threshold network flow games [3,4] on hypergraphs.