Computational Complexity in Additive Hedonic Games

Sung, Shao Chin; Dimitrov, Dinko

doi:10.2139/ssrn.1318329

Cited by 27 publications

(42 citation statements)

References 62 publications

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“…This fact does not imply that checking the existence of a core stable partition is NP-hard. Recently, Sung and Dimitrov (2010) showed that for ASHGs checking whether a core stable or strict core stable partition exists is NP-hard in the strong sense. Their reduction relied on the asymmetry of the players' preferences.…”

Section: Core and Strict Corementioning

confidence: 99%

Computing desirable partitions in additively separable hedonic games

Aziz

Brandt

Seedig

2013

Artificial Intelligence

103

124

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An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. In this paper, we solve various open problems concerning the computational complexity of stable partitions in additively separable hedonic games. First, we propose a polynomial-time algorithm to compute a contractually individually stable partition. This contrasts with previous results such as the NP-hardness of computing individually stable or Nash stable partitions. Secondly, we prove that checking whether the core or the strict core exists is NP-hard in the strong sense even if the preferences of the players are symmetric. Finally, it is shown that verifying whether a partition consisting of the grand coalition is contractually strict core stable or Pareto optimal is coNP-complete.

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Section: Core and Strict Corementioning

confidence: 99%

Computing desirable partitions in additively separable hedonic games

Aziz

Brandt

Seedig

2013

Artificial Intelligence

103

124

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“…More precisely, he shows that determining whether there is a Nash stable, an individually stable, and a core stable coalition structure is NP-complete. In [24], Sung and Dimitrov show that the same results hold for ASHG. Aziz et al investigate the computational complexity for many concepts including the above five solution concepts [4].…”

Section: Introductionmentioning

confidence: 64%

Computational Complexity of Hedonic Games on Sparse Graphs

Hanaka

Kiya

Maei

et al. 2019

PRIMA 2019: Principles and Practice of Multi-Agent Systems

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The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash stable solution, a maximum utilitarian solution, and a maximum egalitarian solution in ASHGs on sparse graphs including boundeddegree graphs, bounded-treewidth graphs, and near-planar graphs. For example, we show that finding a maximum egalitarian solution is weakly NP-hard even on graphs of treewidth 2, whereas it can be solvable in polynomial time on trees. Moreover, we give a pseudo fixed parameter algorithm when parameterized by treewidth.

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“…Fractional hedonic games are related to additively separable hedonic games [see, e.g., , Olsen, 2009, Sung and Dimitrov, 2010. In both fractional hedonic games and additively separable hedonic games, each player ascribes a cardinal value to every other player.…”

Section: Related Workmentioning

confidence: 99%

Fractional Hedonic Games

Aziz

Brandl

Brandt

et al. 2019

ACM Trans. Econ. Comput.

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The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is non-empty and provide algorithms for computing a core stable outcome. By contrast, we show that the core may be empty in other cases, and that it is computationally hard in general to decide non-emptiness of the core. the partitions in the strict core, and give a polynomial time algorithm to compute a unique finest partition in the strict core.• We discuss how computing desirable outcomes in fractional hedonic games provides an interesting game-theoretic perspective to community detection [see, e.g., Fortunato, 2010, Newman, 2004 and network clustering. 2 RELATED WORKFractional hedonic games are related to additively separable hedonic games [see, e.g., , Olsen, 2009, Sung and Dimitrov, 2010. In both fractional hedonic games and additively separable hedonic games, each player ascribes a cardinal value to every other player. In additively separable hedonic games, utility in a coalition is derived by adding the values for the other players. By contrast, in fractional hedonic games, utility in a coalition is derived by adding the values for the other players and then dividing the sum by the total number of players in the coalition. Although conceptually, additively separable and fractional hedonic games are similar, their formal properties are quite different. As neither of the two models is obviously superior, this shows how slight modeling decisions may affect the formal analysis. For example, in unweighted and undirected graphs, the grand coalition is trivially core stable for additively separable hedonic games.On the other hand, this is not the case for fractional hedonic games. 3 A fractional hedonic game approach to social networks with only non-negative weights may help detect like-minded and densely connected communities. In comparison, when the network only has non-negative weights for the edges, any reasonable solution for the corresponding additively separable hedonic game returns the grand coalition, which is not informative. The difference between additively separable and fractional hedonic games is reminiscent of some issues in population ethics (see, e.g., Arrhenius et al., 2017), which concerns the evaluation of states of the world with different numbers of individuals alive. Two prominent principles in population ethics are total utilitarianism and average utilitarianism. The former claims that a state of the world is better than another...

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Computational Complexity in Additive Hedonic Games

Cited by 27 publications

References 62 publications

Computing desirable partitions in additively separable hedonic games

Computing desirable partitions in additively separable hedonic games

Computational Complexity of Hedonic Games on Sparse Graphs

Fractional Hedonic Games

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