中立型约束下享乐对策的个体和群体稳定性
Individual and Group Stability in Neutral Restrictions of Hedonic Games
摘要：
我们考虑一类称为享乐博弈的联盟形成博弈，即，参与者的效用完全由参与者所属的联盟决定的博弈。我们首先定义了一类子集可加享乐博弈，并证明了它们与享乐博弈具有相同的表示能力。然后，我们定义了一个子集加性享乐博弈的限制，我们称之为子集中性享乐博弈，并推广了Bogomolnaia和Jackson（2002）的结果，证明了在这样的博弈中存在纳什稳定分区和个体稳定分区。我们还考虑了中立匿名享乐游戏，并表明它们形成了子集加性享乐游戏的一个子类。最后，我们展示了存在一个核心稳定的分区，也是单独稳定的中立匿名享乐游戏展示一个算法来计算这样的分区。
英文摘要：
We consider a class of coalition formation games called hedonic games, i.e., games in which the utility of a player is completely determined by the coalition that the player belongs to. We first define the class of subset-additive hedonic games and show that they have the same representation power as the class of hedonic games. We then define a restriction of subset-additive hedonic games that we call subset-neutral hedonic games and generalize a result by Bogomolnaia and Jackson (2002) by showing the existence of a Nash stable partition and an individually stable partition in such games. We also consider neutrally anonymous hedonic games and show that they form a subclass of the subset-additive hedonic games. Finally, we show the existence of a core stable partition that is also individually stable in neutrally anonymous hedonic games by exhibiting an algorithm to compute such a partition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
