On the complexity of cooperative solution concepts
Mathematics of Operations Research
Coalitions among computationally bounded agents
Artificial Intelligence - Special issue on economic principles of multi-agent systems
Methods for task allocation via agent coalition formation
Artificial Intelligence
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
Multi-attribute coalitional games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A kernel-oriented model for coalition-formation in general environments: implementation and results
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
An analysis of the shapley value and its uncertainty for the voting game
AMEC'05 Proceedings of the 2005 international conference on Agent-Mediated Electronic Commerce: designing Trading Agents and Mechanisms
A linear approximation method for the Shapley value
Artificial Intelligence
An anytime approximation method for the inverse Shapley value problem
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
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
Power in threshold network flow games
Autonomous Agents and Multi-Agent Systems
Manipulating the quota in weighted voting games
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
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
A heuristic approximation method for the Banzhaf index for voting games
Multiagent and Grid Systems
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The Shapley value is one of the key solution concepts for coalition games. Its main advantage is that it provides a unique and fair solution, but its main problem is that, for many coalition games, the Shapley value cannot be determined in polynomial time. In particular, the problem of finding this value for the voting game is known to be #P-complete in the general case. However, in this paper, we show that there are some specific voting games for which the problem is computationally tractable. For other general voting games, we overcome the problem of computational complexity by presenting a new randomized method for determining the approximate Shapley value. The time complexity of this method is linear in the number of players. We also show, through empirical studies, that the percentage error for the proposed method is always less than 20% and, in most cases, less than 5%.