Computational Complexity of Weighted Threshold Games

Edith Elkind, Leslie Ann Goldberg, Paul Goldberg, Michael Wooldridge

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 division of payoffs to coalition members (an imputation) that is fair. We investigate the computational complexity of such questions for weighted threshold games. We study the core, the least core, and the nucleolus, distinguishing those problems that are polynomial-time computable from those that are NP-hard, and providing pseudopolynomial and approximation algorithms for the NP-hard problems.

Subjects: 7.1 Multi-Agent Systems; 9.2 Computational Complexity

Submitted: Apr 23, 2007

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