NP-completeness for calculating power indices of weighted majority games
نویسندگان
چکیده
In this paper, we prove that both problems for calculating the Banzhaf power index and the Shapley-Shubik power index for weighted majority games are NP-complete.
منابع مشابه
Easy weighted majority games
In a weighted majority game each player has a positive integer weight and there is a positive integer quota. A coalition of players is winning (losing) if the sum of the weights of its members exceeds (does not exceed) the quota. A player is pivotal for a coalition if her omission changes it from a winning to a losing one. Most game theoretic measures of the power of a player involve the comput...
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Weighted threshold games are coalitional games in which each player has a weight (intuitively corresponding to its voting power), and a coalition is successful if the sum of its weights exceeds a given threshold. Key questions in coalitional games include finding coalitions that are stable (in the sense that no member of the coalition has any rational incentive to leave it), and finding a divis...
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Power indices of weighted majority games are measures of the effects of parties on the voting in a council. Among the many kinds of power indices, Banzhaf index, Shapley-Shubik index and Deegan-Packel index have been studied well. For computing these power indices, dynamic programming algorithms had been proposed. The time complexities of these algorithms are O(nq), O(nq), and O(nq), respective...
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A ‘power index’ is a concept in cooperative game theory. Power indices are used as a measure for the influence that a player has in a certain class of cooperative games called simple games. As the title says, this is a survey on how to compute these power indices. Generally speaking, computing these indices is a tedious task, even for relatively small cooperative games. It is certainly intracta...
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 263 شماره
صفحات -
تاریخ انتشار 2001