We consider graph-based hedonic games such as simple symmetric fractional hedonic games and social distance games, where a group of utility maximizing players have hedonic preferences over the players' set, and wish to be partitioned into clusters so that they are grouped together with players they prefer. The players are nodes in a connected graph and their preferences are defined so that shorter graph distance implies higher preference. We are interested in Nash equilibria of such games, where no player has an incentive to unilaterally deviate to another cluster, and we focus on the notion of the price of stability. We present new and improved bounds on the price of stability for several graph classes, as well as for a slightly modified utility function.

我们考虑基于图的享乐游戏，例如简单的对称分数享乐游戏和社交距离游戏，其中一群效用最大化的玩家对享乐者的偏好具有享乐偏好，希望将其划分为多个集群，以便将它们与玩家分组在一起他们更喜欢。参与者是连接图中的节点，并且定义了它们的首选项，因此较短的图距离意味着较高的首选项。我们对此类游戏的纳什均衡感兴趣，在这种均衡中，没有玩家有动机单方面偏离另一个集群，因此我们关注稳定性价格的概念。我们为几个图类以及经过稍微修改的效用函数提供了关于稳定性价格的新的和改进的界限。