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Introduction to algorithms
On the complexity of cooperative solution concepts
Mathematics of Operations Research
Coalition, cryptography, and stability: mechanisms for coalition formation in task oriented domains
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Coalitions among computationally bounded agents
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Methods for task allocation via agent coalition formation
Artificial Intelligence
Coalition structure generation with worst case guarantees
Artificial Intelligence
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
A Kernel-Oriented Model for Autonomous-Agent Coalition-Formation in General Environments
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Computing Power Indices for Large Voting Games
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Marginal contribution nets: a compact representation scheme for coalitional games
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Multi-attribute coalitional games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
An algorithm for distributing coalitional value calculations among cooperating agents
Artificial Intelligence
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
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Computational complexity of weighted threshold games
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
An approach for multi-objective categorization based on the game theory and Markov process
Applied Soft Computing
Deploying power grid-integrated electric vehicles as a multi-agent system
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
Manipulating the quota in weighted voting games
Artificial Intelligence
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
Automated analysis of weighted voting games
Proceedings of the 13th International Conference on Electronic Commerce
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
Efficient computation of the shapley value for game-theoretic network centrality
Journal of Artificial Intelligence Research
Using coalitional games to detect communities in social networks
WAIM'13 Proceedings of the 14th international conference on Web-Age Information Management
A game theory based approach for community detection in social networks
BNCOD'13 Proceedings of the 29th British National conference on Big Data
On random quotas and proportional representation in weighted voting games
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Internal structure of coalitions in competitive and altruistic graphical coalitional games
Automatica (Journal of IFAC)
A heuristic approximation method for the Banzhaf index for voting games
Multiagent and Grid Systems
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The Shapley value is a key solution concept for coalitional games in general and voting games in particular. Its main advantage is that it provides a unique and fair solution, but its main drawback is the complexity of computing it (e.g., for voting games this complexity is #p-complete). However, given the importance of the Shapley value and voting games, a number of approximation methods have been developed to overcome this complexity. Among these, Owen's multi-linear extension method is the most time efficient, being linear in the number of players. Now, in addition to speed, the other key criterion for an approximation algorithm is its approximation error. On this dimension, the multi-linear extension method is less impressive. Against this background, this paper presents a new approximation algorithm, based on randomization, for computing the Shapley value of voting games. This method has time complexity linear in the number of players, but has an approximation error that is, on average, lower than Owen's. In addition to this comparative study, we empirically evaluate the error for our method and show how the different parameters of the voting game affect it. Specifically, we show the following effects. First, as the number of players in a voting game increases, the average percentage error decreases. Second, as the quota increases, the average percentage error decreases. Third, the error is different for players with different weights; players with weight closer to the mean weight have a lower error than those with weight further away. We then extend our approximation to the more general k-majority voting games and show that, for n players, the method has time complexity O(k^2n) and the upper bound on its approximation error is O(k^2/n).