Hedonic games are a prominent model of coalition formation, in which each agent’s utility only depends on the coalition she resides. The subclass of hedonic games that models the formation of general partnerships (Larson 2018), where all affiliates receive the same utility, is referred to as hedonic games with common ranking property (HGCRP). Aside from their economic motivation, HGCRP came into prominence since they are guaranteed to have core stable solutions that can be found efficiently (Farrell and Scotchmer Q. J. Econ. 103(2), 279–297 1988). We improve upon existing results by proving that every instance of HGCRP has a solution that is Pareto optimal, core stable, and individually stable. The economic significance of this result is that efficiency is not to be totally sacrificed for the sake of stability in HGCRP. We establish that finding such a solution is NP-hard even if the sizes of the coalitions are bounded above by 3; however, it is polynomial time solvable if the sizes of the coalitions are bounded above by 2. We show that the gap between the total utility of a core stable solution and that of the socially-optimal solution (OPT) is bounded above by n, where n is the number of agents, and that this bound is tight. Our investigations reveal that computing OPT is inapproximable within better than \(O(n^{1-\epsilon })\) for any fixed \(\epsilon > 0\), and that this inapproximability lower bound is polynomially tight. However, OPT can be computed in polynomial time if the sizes of the coalitions are bounded above by 2.

享乐博弈是联盟形成的一个重要模型，其中每个智能体的效用仅取决于她所在的联盟。对普通合伙企业的形成进行建模的享乐博弈子类（Larson 2018），其中所有附属公司都获得相同的效用，被称为具有共同排名属性的享乐博弈（HGCRP）。除了经济动机之外，HGCRP 之所以引人注目，是因为他们保证拥有可以有效找到的核心稳定解决方案（Farrell 和 Scotchmer QJ Econ. 103(2), 279–297 1988)。我们通过证明 HGCRP 的每个实例都有一个帕累托最优、核心稳定和个体稳定的解决方案来改进现有结果。这一结果的经济意义在于，不能为了HGCRP的稳定性而完全牺牲效率。我们确定，即使联盟的大小以 3 以上为界，找到这样的解决方案也是NP 困难的；然而，如果联盟的大小以 2 为界，则它是多项式时间可解的。我们表明，核心稳定解决方案的总效用与社会最优解决方案 (OPT) 的总效用之间的差距以 n 为界，其中n是代理的数量，并且这个界限是紧密的。我们的研究表明，对于任何固定的\(\epsilon > 0\) ，计算 OPT 的不可近似性优于\(O(n^{1-\epsilon })\)，并且这种不可近似性下界是多项式紧的。然而，如果联盟的大小以 2 为界，则可以在多项式时间内计算 OPT。