NP-completeness of some problems concerning voting games
International Journal of Game Theory
On the complexity of cooperative solution concepts
Mathematics of Operations Research
A new polynomial-time algorithm for linear programming
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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
On encoding and enumerating threshold functions
IEEE Transactions on Neural Networks
False-name manipulations in weighted voting games
Journal of Artificial Intelligence Research
Manipulating the quota in weighted voting games
Artificial Intelligence
The inverse shapley value problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Complementary cooperation, minimal winning coalitions, and power indices
Theoretical Computer Science
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In many multiagent settings, situations arise in which agents must collectively make decisions while not every agent is supposed to have an equal amount of influence in the outcome of such a decision. Weighted voting games are often used to deal with these situations. The amount of influence that an agent has in a weighted voting game can be measured by means of various power indices. This paper studies the problem of finding a weighted voting game in which the distribution of the influence among the agents is as close as possible to a given target value. We propose a method to exactly solve this problem. This method relies on a new efficient procedure for enumerating weighted voting games of a fixed number of agents. The enumeration algorithm we propose works by exploiting the properties of a specific partial order over the class of weighted voting games. The algorithm enumerates weighted voting games of a fixed number of agents in time exponential in the number of agents, and polynomial in the number of games output. As a consequence we obtain an exact anytime algorithm for designing weighted voting games.