Computational Complexity in Additive Hedonic Games

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense

Size Monotonicity and Stability of the Core in Hedonic Games

We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.Core, Hedonic Games, Monotonicity, Stable Sets

A Taxonomy of Myopic Stability Concepts for Hedonic Games

We present a taxonomy of myopic stability concepts for hedonic games in terms of deviations, and discuss the status of the existence problems of stable coalition tructures. In particular, we show that contractual strictly core stable coalition tructures always exist, and provide su¢ cient conditions for the existence of con- ractually Nash stable and weak individually stable coalition structures on the class of separable games.Coalition formation, Hedonic games, Separability, Taxonomy

Computational Complexity in Additive Hedonic Games

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense.Additive Preferences, Coalition Formation, Computational Complexity, Hedonic Games, NP-hard, NP-complete

On core membership testing for hedonic coalition formation games

We are concerned with the problem of core membership testing for hedonic coalition formation games, which is to decide whether a certain coalition structure belongs to the core of a given game. We show that this problem is co-NP complete when players' preferences are additive.additivity, coalition formation, core, co-NP completeness, hedonic games

A taxonomy of myopic stability concepts for hedonic games

We present a taxonomy of myopic stability concepts for hedonic games in terms of deviations, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and provide sufficient conditions for the existence of contractually Nash stable and weak individually stable coalition structures on the class of separable games.coalition formation, hedonic games, separability, taxonomy

Procedural group identification

In this paper we axiomatically characterize two recursive procedures for defining a social group. The first procedure starts with the set of all individuals who are defined by everyone in the society as group members, while the starting point of the second procedure is the set of all individuals who define themselves as members of the social group. Both procedures expand these initial sets by adding individuals who are considered to be appropriate group members by someone in the corresponding initial set, and continue inductively un- til there is no possibility of expansion any more.consensus, liberalism, procedure, social identity

Constraints on Unparticle Interactions from Invisible Decays of Z, Quarkonia and Neutrinos

Unparticles (\U) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrinos. The constraints on the unparticle interaction scale \Lambda_\U are very sensitive to the dimension d_\U of the unparticles. From invisible $Z$ and $V$ decays, we find that with d_\U close to 1 for vector \U, the unparticle scale \Lambda_\U can be more than $10^4$ TeV, and for d_\U around 2, the scale can be lower than one TeV. From invisible neutrino decays, we find that if d_\U is close to 3/2, the scale can be more than the Planck mass, but with d_\U around 2 the scale can be as low as a few hundred GeV. We also study the possibility of using V (Z)\to \gamma + \U to constrain unparticle interactions, and find that present data give weak constraints.Comment: 12 pages, 4 figures, version to appear in JHEP