1,089 research outputs found
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
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
Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games
Additively separable hedonic games and fractional hedonic games have received
considerable attention. They are coalition forming games of selfish agents
based on their mutual preferences. Most of the work in the literature
characterizes the existence and structure of stable outcomes (i.e., partitions
in coalitions), assuming that preferences are given. However, there is little
discussion on this assumption. In fact, agents receive different utilities if
they belong to different partitions, and thus it is natural for them to declare
their preferences strategically in order to maximize their benefit. In this
paper we consider strategyproof mechanisms for additively separable hedonic
games and fractional hedonic games, that is, partitioning methods without
payments such that utility maximizing agents have no incentive to lie about
their true preferences. We focus on social welfare maximization and provide
several lower and upper bounds on the performance achievable by strategyproof
mechanisms for general and specific additive functions. In most of the cases we
provide tight or asymptotically tight results. All our mechanisms are simple
and can be computed in polynomial time. Moreover, all the lower bounds are
unconditional, that is, they do not rely on any computational or complexity
assumptions
Precise Complexity of the Core in Dichotomous and Additive Hedonic Games
Hedonic games provide a general model of coalition formation, in which a set
of agents is partitioned into coalitions, with each agent having preferences
over which other players are in her coalition. We prove that with additively
separable preferences, it is -complete to decide whether a core- or
strict-core-stable partition exists, extending a result of Woeginger (2013).
Our result holds even if valuations are symmetric and non-zero only for a
constant number of other agents. We also establish -completeness of
deciding non-emptiness of the strict core for hedonic games with dichotomous
preferences. Such results establish that the core is much less tractable than
solution concepts such as individual stability.Comment: ADT-2017, 15 pages in LNCS styl
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
Optimal Partitions in Additively Separable Hedonic Games
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
-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.Comment: 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 Lisbo
Hedonic Games with Graph-restricted Communication
We study hedonic coalition formation games in which cooperation among the
players is restricted by a graph structure: a subset of players can form a
coalition if and only if they are connected in the given graph. We investigate
the complexity of finding stable outcomes in such games, for several notions of
stability. In particular, we provide an efficient algorithm that finds an
individually stable partition for an arbitrary hedonic game on an acyclic
graph. We also introduce a new stability concept -in-neighbor stability- which
is tailored for our setting. We show that the problem of finding an in-neighbor
stable outcome admits a polynomial-time algorithm if the underlying graph is a
path, but is NP-hard for arbitrary trees even for additively separable hedonic
games; for symmetric additively separable games we obtain a PLS-hardness
result
Simple Priorities and Core Stability in Hedonic Games
In this paper we study hedonic games where each player views every other player either as a friend or as an enemy.Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered.It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games.Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard.We examine also the relationship between our domain restrictions and some su.cient conditions for non-emptiness of the core already known in the literature.core;stability;games
Simple Priorities and Core Stability in Hedonic Games
In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions and some sufficient conditions for non-emptiness of the core already known in the literature.coalition formation, core stability, hedonic games, priority
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