Computing the nucleolus of weighted voting games in pseudo-polynomial time

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In cooperative games, players have a possibility to form different coalitions. This leads to the questions about ways to motivate all players to collaborate, i.e. to motivate the players to form the so-called grand coalition. One of such ways is captured by the concept of nucleolus, which dates back to Babylonian Talmud. Weighted voting games form a class of cooperative games, that are often used to model decision making processes in parliaments. In this paper, we provide an algorithm for computing the nucleolus for an instance of a weighted voting game in pseudo-polynomial time. This resolves an open question posed by Elkind et al. (Ann Math Artif Intell 56(2), 109–131, 2007).