The polynomial-time hierarchy and sparse oracles
Journal of the ACM (JACM)
NP-completeness of some problems concerning voting games
International Journal of Game Theory
Probabilistic polynomial time is closed under parity reductions
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A randomized method for the shapley value for the voting game
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
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
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Coalitional games in open anonymous environments
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
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
Multimode control attacks on elections
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Collusion in VCG path procurement auctions
WINE'10 Proceedings of the 6th international conference on Internet and network economics
The good, the bad and the cautious: safety level cooperative games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
A cooperative approach to collusion in auctions
ACM SIGecom Exchanges
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
Rip-off: playing the cooperative negotiation game
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
The Shapley value as a function of the quota in weighted voting games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
The inverse shapley value problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Proof systems and transformation games
Annals of Mathematics and Artificial Intelligence
Computing cooperative solution concepts in coalitional skill games
Artificial Intelligence
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Weighted voting games provide a popular model of decision making in multiagent systems. Such games are described by a set of players, a list of players' weights, and a quota; a coalition of the players is said to be winning if the total weight of its members meets or exceeds the quota. The power of a player in such games is traditionally identified with her Shapley-Shubik index or her Banzhaf index, two classical power measures that reflect the player's marginal contributions under different coalition formation scenarios. In this paper, we investigate by how much the central authority can change a player's power, as measured by these indices, by modifying the quota. We provide tight upper and lower bounds on the changes in the individual player's power that can result from a change in quota. We also study how the choice of quota can affect the relative power of the players. From the algorithmic perspective, we provide an efficient algorithm for determining whether there is a value of the quota that makes a given player a dummy, i.e., reduces his power (as measured by both indices) to 0. On the other hand, we show that checking which of the two values of the quota makes this player more powerful is computationally hard, namely, complete for the complexity class PP, which is believed to be significantly more powerful than NP.