Computational Complexity of Hedonic Games on Sparse Graphs

解决关于利他主义霍德onic游戏核心稳定性的四个开放问题

Solving Four Open Problems about Core Stability in Altruistic Hedonic Games

本文解决四个关于利他主义霍德onic游戏核心稳定性的开放问题，证明其复杂性为coNP完全。

可加可分享乐博弈中强受欢迎性的复杂性

Complexity of Strong Popularity in Additively Separable Hedonic Games

该研究针对可加可分享乐博弈（ASHGs），证明判定其中强受欢迎划分的存在性为PCW完全问题，解决了相关开放问题，明确了该问题的计算复杂性。

Stable partitions in additively separable hedonic games

An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. In this paper, we solve various open problems concerning the computational complexity of stable partitions in additively separable hedonic games. First, we propose a polynomial-time algorithm to compute a contractually individually stable partition. This contrasts with previous results such as the NP-hardness of computing individually stable or Nash stable partitions. Secondly, we prove that checking whether the core or the strict core exists is NP-hard in the strong sense eve…

低树宽可加可分快乐博弈中的核心稳定性

Core Stability in Additively Separable Hedonic Games of Low Treewidth

本文从结构参数化复杂性角度，利用树宽等图论参数，重新研究了可加可分快乐博弈（ASHG）中核心稳定性的计算复杂性，该问题在一般情况下的求解与验证均为难解问题。

Hedonic Games and Treewidth Revisited

We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an edge-weighted digraph $G=(V,E)$, and the weight of an arc $uv$ denotes the utility $u$ gains by being in the same coalition as $v$. We focus on (arguably) the most basic stability question about such a game: given a graph, does a Nash stable solution exist and can we find it efficiently? We study the (parameterized) complexity of ASHG stability when the underlying gra…

计算社会选择：参数化复杂度与挑战

Computational Social Choice: Parameterized Complexity and Challenges

该研究综述了计算社会选择领域的多赢家确定、享乐博弈两大关键问题，聚焦其参数化复杂度，并提出了相关研究挑战。