Optimal Partitions in Additively Separable Hedonic Games
Haris Aziz, Felix Brandt, Hans Georg Seedig
备注：
11 pages; A preliminary version of this work was invited for presentation in the session `Cooperative Games and Combinatorial Optimization' at the 24th European Conference on Operational Research (EURO 2010) in Lisbon
We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is $Σ_{2}^{p}$-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.
Individual Rationality in Constrained Hedonic Games: Additively Separable and Fractional Preferences
Czech Technical University in Prague（布拉格捷克理工大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Charles University（查理大学）；AGH University of Krakow（克拉科夫AGH科技大学）
Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals
AGH University of Krakow（克拉科夫 AGH 科技大学）；Czech Technical University in Prague（布拉格捷克理工大学）；ELTE Centre for Economic and Regional Studies（布达佩斯罗兰大学经济区域研究中心）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
