We introduce the notion of linearly representable games. Broadly speaking, these are TU games that can be described by as many parameters as the number of players, like weighted voting games, airport games, or bankruptcy games. We show that the Shapley value calculation is pseudo-polynomial for linearly representable games. This is a generalization of many classical and recent results in the literature. Our method naturally turns into a strictly polynomial algorithm when the parameters are polynomial in the number of players.

翻译：本文引入线性可表示博弈的概念。广义而言，这类TU博弈可通过与参与者数量相同的参数进行描述，例如加权投票博弈、机场博弈或破产博弈。我们证明对于线性可表示博弈，Shapley值的计算具有伪多项式时间复杂度。该结论推广了文献中诸多经典及最新研究成果。当参数规模关于参与者数量呈多项式增长时，我们的方法可自然转化为严格多项式算法。