An independent set game is a cooperative game defined on graphs and dealing with profit-sharing in maximum independent set problems. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for population monotonic allocation schemes in independent set games. Moreover, our characterization can be verified efficiently.

翻译：独立设定游戏是一种在图表上定义的合作游戏,它处理的是最大独立设定问题的利润分享。 人口单调分配计划是一条规则,规定如何在参与者之间分享每个联盟的利润,这样当联盟扩大时,每个参与者都得到更好的待遇。 在本文中,我们为独立设定游戏中的人口单调分配计划提供了必要和充分的定性。此外,我们的定性可以有效验证。