We investigate Tiered Coalition Formation Games (TCFGs), a cooperative game inspired by the stratification of Pokémon on the fan website, Smogon. It is known that, under match-up oriented preferences, Nash and core stability are equivalent. We previously introduced a notion of socially conscious stability for TCFGs, and introduced a game variant with fixed k-length tier lists. In this work we show that in tier lists under match-up oriented preferences, socially conscious stability is equivalent to Nash stability and to core stability, but in k-tier lists, the three stability notions are distinct. We also give a necessary condition for tier list stability in terms of robustness (the minimum in-tier utility of an agent). We introduce a notion of approximate Nash stability and approximately socially conscious stability, and provide experiments on the empirical run time of our k-tier local search algorithm, and the performance of our algorithms for generating approximately socially consciously stable tier lists.

我们研究了 Tiered Coalition Formation Games (TCFGs)，这是一款受粉丝网站 Smogon 上神奇宝贝分层启发而设计的合作游戏。众所周知，在以匹配为导向的偏好下，纳什和核心稳定性是等价的。我们之前为 TCFG 引入了社会意识稳定性的概念，并引入了具有固定k长度层级列表的游戏变体。在这项工作中，我们表明，在以匹配为导向的偏好下的层级列表中，社会意识稳定性等同于纳什稳定性和核心稳定性，但在k层级列表中，这三个稳定性概念是不同的。我们还从鲁棒性（代理的最小层内效用）方面给出了层列表稳定性的必要条件。我们引入了近似纳什稳定性和近似社会意识稳定性的概念，并提供了关于我们的k层局部搜索算法的经验运行时间的实验，以及我们的算法用于生成近似社会意识稳定层列表的性能。