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

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