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

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

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

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

On top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation, common ranking property, hedonic games, semistrict core, top coalition property

Hedonic coalition formation games: A new stability notion

Cataloged from PDF version of article.This paper studies hedonic coalition formation games where each player's preferences rely only upon the members of her coalition. A new stability notion under free exit-free entry membership rights, referred to as strong Nash stability, is introduced which is stronger than both core and Nash stabilities studied earlier in the literature. Strong Nash stability has an analogue in non-cooperative games and it is the strongest stability notion appropriate to the context of hedonic coalition formation games. The weak top-choice property is introduced and shown to be sufficient for the existence of a strongly Nash stable partition. It is also shown that descending separable preferences guarantee the existence of a strongly Nash stable partition. Strong Nash stability under different membership rights is also studied. (C) 2011 Elsevier B.V. All rights reserved

Top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation

Enemies and Friends in Hedonic Games: Individual Deviations, Stability and Manipulation

We consider hedonic games with separable preferences, and explore the existence of stable coalition structures if only individual deviations are allowed.For two natural subdomains of separable preferences, namely preference domains based on (1) aversion to enemies and (2) appreciation of friends, we show that an individually stable coalition structure always exist, and a Nash stable coalition structure exists when mutuality is imposed.Moreover, we show that on the domain of separable preferences a contractual individually stable coalition structure can be obtained in polynomial time.Finally, we prove that, on each of the two subdomains, the corresponding algorithm that we use for finding Nash stable and individually stable coalition structures turns out to be strategy-proof.additive separability;coalition formation;hedonic games;stability;strategy-proofness