On the computational complexity of weighted voting games

Coalitional games provide a useful tool for modeling cooperation in multiagent systems. An important special class of coalitional games is weighted voting games, in which each player has a weight (intuitively corresponding to its contribution), and a coalition is successful if the sum of its members' weights meets or exceeds a given threshold. A key question in coalitional games is finding coalitions and payoff division schemes that are stable, i.e., no group of players has any rational incentive to leave. In this paper, we investigate the computational complexity of stability-related questions for weighted voting games. We study problems involving the core, the least core, and the nucleolus, distinguishing those that are polynomial-time computable from those that are NP-hard or coNP-hard, and providing pseudopolynomial and approximation algorithms for some of the computationally hard problems.