215 research outputs found
Stable Coalition Structures in Simple Games with Veto Control
In this paper we study hedonic coalition formation games in which players' preferences over coalitions are induced by a semi-value of a monotonic simple game with veto control.We consider partitions of the player set in which the winning coalition contains the union of all minimal winning coalitions, and show that each of these partitions belongs to the strict core of the hedonic game. Exactly such coalition structures constitute the strict core when the simple game is symmetric.Provided that the veto player set is not a winning coalition in a symmetric simple game, then the partition containing the grand coalition is the unique strictly core stable coalition structure.Banzhaf value;hedonic game;semi-value;Shapley value;simple game;strict core
Stable coalition structures in simple games with veto control
In this paper we study hedonic coalition formation games in which players. preferences over coalitions are induced by a semi-value of a monotonic simple game with veto control. We consider partitions of the player set in which the winning coalition contains the union of all minimal winning coalitions, and show that each of these partitions belongs to the strict core of the hedonic game. Exactly such coalition structures constitute the strict core when the simple game is symmetric. Provided that the veto player set is not a winning coalition in a symmetric simple game, then the partition containing the grand coalition is the unique strictly core stable coalition structure.Banzhaf value, hedonic game, semi-value, Shapley value, simple game, strict core
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
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
Boolean Hedonic Games
We study hedonic games with dichotomous preferences. Hedonic games are
cooperative games in which players desire to form coalitions, but only care
about the makeup of the coalitions of which they are members; they are
indifferent about the makeup of other coalitions. The assumption of dichotomous
preferences means that, additionally, each player's preference relation
partitions the set of coalitions of which that player is a member into just two
equivalence classes: satisfactory and unsatisfactory. A player is indifferent
between satisfactory coalitions, and is indifferent between unsatisfactory
coalitions, but strictly prefers any satisfactory coalition over any
unsatisfactory coalition. We develop a succinct representation for such games,
in which each player's preference relation is represented by a propositional
formula. We show how solution concepts for hedonic games with dichotomous
preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic
and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen,
Norway, July 27-30, 201
The Core-Partition of Hedonic Games.
La classe des jeux hédonistiques purs modélisent des situations d’interactions sociales où l’utilité de chaque joueur dépend seulement de l’identité du groupe auquel il appartient. L’article propose une condition nécessaire et suffisante pour l’existence de partition stable, au sens du cœur, dans les jeux hédonistiques. La condition, appelée balancement avec pivot, raffine la condition usuelle de balancement. Elle fait notamment appel à des distributions pivots qui, à chaque coalition, associe un sous-groupe de joueurs dans la coalition. Nous unifions les résultats de la littérature sur les partitions stables en identifiant des distributions pivots adéquates.In a hedonic game the preference relation of each player is defined on the set of coalitions that contain the player. The paper provides a necessary and sufficient condition for core-partition existence in a hedonic game. The condition is based on a new concept of balancedness, called pivotal balancedness, involving subsets of players in any given family of coalitions. Pivotal balancedness highlights the existence of key players in each coalition that are relevant for the existence of a core-partition.Hedonic Game; Group Formation; Core-Partition; Balancedness; Jeu hédonistique; Formation de groupes; Coeur-partition; Balancement;
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
Forming Probably Stable Communities with Limited Interactions
A community needs to be partitioned into disjoint groups; each community
member has an underlying preference over the groups that they would want to be
a member of. We are interested in finding a stable community structure: one
where no subset of members wants to deviate from the current structure. We
model this setting as a hedonic game, where players are connected by an
underlying interaction network, and can only consider joining groups that are
connected subgraphs of the underlying graph. We analyze the relation between
network structure, and one's capability to infer statistically stable (also
known as PAC stable) player partitions from data. We show that when the
interaction network is a forest, one can efficiently infer PAC stable coalition
structures. Furthermore, when the underlying interaction graph is not a forest,
efficient PAC stabilizability is no longer achievable. Thus, our results
completely characterize when one can leverage the underlying graph structure in
order to compute PAC stable outcomes for hedonic games. Finally, given an
unknown underlying interaction network, we show that it is NP-hard to decide
whether there exists a forest consistent with data samples from the network.Comment: 11 pages, full version of accepted AAAI-19 pape
Coalition formation in simple games: The semistrict core
We consider the class of proper monotonic simple games and study coalition formation when an exogenous share vector and a solution concept are combined to guide the distribution of coalitional worth. Using a multiplicative composite solution, we induce players' preferences over coalitions in a hedonic game, and present conditions under which the semistrict core of the game is nonempty.coalition formation, semistrict core, simple games, winning coalitions
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