NP-completeness of some problems concerning voting games
International Journal of Game Theory
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
Artificial Intelligence - Special issue on economic principles of multi-agent systems
Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computing Power Indices for Large Voting Games
Management Science
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
A linear approximation method for the Shapley value
Artificial Intelligence
Methods for task allocation via agent coalition formation
Artificial Intelligence
Complexity of constructing solutions in the core based on synergies among coalitions
Artificial Intelligence
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
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
Automated analysis of weighted voting games
Proceedings of the 13th International Conference on Electronic Commerce
Hi-index | 0.00 |
The Banzhaf index is a well known and widely used index for measuring the power a player has in a voting game. However, the problem of computing this index is computationally hard. To overcome this problem, a number of approximation methods were developed for one majority voting games. While it may be possible to extend some of these to k-majority games which are generalized versions of one majority games, to date, there has been no performance analysis of these methods in the context of the Banzhaf index for k-majority games. In this paper, we fill this gap, by first presenting an approximation method for the Banzhaf index for k-majority games. This is a heuristic method that uses randomization to estimate an approximate. We then show that this method is computationally feasible. Finally, we evaluate its performance by analyzing its error of approximation, and show how the error varies with k. Specifically, we show that the average percentage error increases from 15% for games with k=1 to 30% for games with k=5.