Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A linear approximation method for the Shapley value
Artificial Intelligence
Approximating power indices: theoretical and empirical analysis
Autonomous Agents and Multi-Agent Systems
A heuristic approximation method for the Banzhaf index for voting games
Multiagent and Grid Systems
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Weighted voting games (WVGs) are an important mechanism for modeling scenarios where a group of agents must reach agreement on some issue over which they have different preferences. However, for such games to be effective, they must be well designed. Thus, a key concern for a mechanism designer is to structure games so that they have certain desirable properties. In this context, two such properties are proper and strong. A game is proper if for every coalition that is winning, its complement is not. A game is strong if for every coalition that is losing, its complement is not. In most cases, a mechanism designer wants games that are both proper and strong. To this end, we first show that the problem of determining whether a game is proper or strong is, in general, np-hard. Then we determine those conditions (that can be evaluated in polynomial time) under which a given WVG is proper and those under which it is strong. Finally, for the general np-hard case, we discuss two different approaches for overcoming the complexity: a deterministic approximation scheme and a randomized approximation method.