论文标题

在具有共同排名属性的享乐游戏中

On Hedonic Games with Common Ranking Property

论文作者

Caskurlu, Bugra, Kizilkaya, Fatih Erdem

论文摘要

享乐游戏是联盟组成的杰出模式,在这种模式下,每个代理商的公用事业都仅取决于她所居住的联盟。享乐游戏的子类建模建立一般合作伙伴关系的形成,其中输出在会员之间同样共享,称为具有共同排名属性(HGCRP)的享乐游戏。除了他们的经济动机外,HGCRP也引起了人们的关注,因为它们可以保证具有可以有效发现的核心稳定解决方案。我们通过证明HGCRP的每个实例都有一个帕累托最佳,核心稳定且单独稳定的解决方案来改善现有结果。这种结果的经济意义在于,为了HGCRP的稳定性,不应完全牺牲效率。我们确定即使联盟的大小在上面的限制为$ 3 $,也可以找到这种解决方案是{\ bf np-hard};但是,如果联盟的尺寸在上面限制为$ 2 $,则可以解决多项式时间。我们表明,核心稳定解决方案的总实用性与社会优势解决方案(OPT)的差距在上面以$ n $为界,其中$ n $是代理的数量,并且这种界限很紧。我们的调查表明,对于任何固定的$ε> 0 $,计算OPT在比$ O(N^{1-ε})$的情况下是不合适的,并且这种不可Ximimibility的下限在多项式上是多项式紧密的。但是,如果联盟的尺寸在上述上方为$ 2 $,则可以在多项式时间内计算OPT。

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, where output is shared equally among affiliates, 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. 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 {\bf 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 $O(n^{1-ε})$ for any fixed $ε> 0$, 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 $2$.

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