Pareto Optimality in Coalition Formation

Aziz, Haris; Brandt, Felix; Harrenstein, Paul

doi:10.1007/978-3-642-24829-0_10

Cited by 28 publications

(57 citation statements)

References 12 publications

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“…Other stability notions in coalition forming games, such as Pareto stability, have also been investigated (Aziz, Brandt, & Harrenstein, 2013;Balliu, Flammini, & Olivetti, 2017b;Elkind et al, 2016). Concerning these stability notions, Elkind et al (2016) study the price of Pareto optimality, that is the ratio between the social welfare in a social welfaremaximizing outcome of the game and the one in a worst Pareto optimal solution.…”

Section: Related Workmentioning

confidence: 99%

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Bilò¹,

Fanelli²,

Flammini³

et al. 2018

jair

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We consider fractional hedonic games, a subclass of coalition formation games that can be succinctly modeled by means of a graph in which nodes represent agents and edge weights the degree of preference of the corresponding endpoints. The happiness or utility of an agent for being in a coalition is the average value she ascribes to its members. We adopt Nash stable outcomes as the target solution concept; that is we focus on states in which no agent can improve her utility by unilaterally changing her own group. We provide existence, efficiency and complexity results for games played on both general and specific graph topologies. As to the efficiency results, we mainly study the quality of the best Nash stable outcome and refer to the ratio between the social welfare of an optimal coalition structure and the one of such an equilibrium as to the price of stability. In this respect, we remark that a best Nash stable outcome has a natural meaning of stability, since it is the optimal solution among the ones which can be accepted by selfish agents. We provide upper and lower bounds on the price of stability for different topologies, both in case of weighted and unweighted edges. Beside the results for general graphs, we give refined bounds for various specific cases, such as triangle-free, bipartite graphs and tree graphs. For these families, we also show how to efficiently compute Nash stable outcomes with provable good social welfare.

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Section: Related Workmentioning

confidence: 99%

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Bilò¹,

Fanelli²,

Flammini³

et al. 2018

jair

View full text Add to dashboard Cite

show abstract

“…In addition, the computational complexity of stable partitions with respect to different notions of stability such as Nash stability, individual stability or core stability has also been considered in the context of additively separable hedonic games, e.g., in the works of Aziz et al (2011) (where also the concept of Pareto optimality is considered), Dimitrov et al (2006) and Olsen (2007). Aziz et al (2013) focus on the computational complexity involved in finding Pareto optimal solutions in hedonic games and variants thereof, including anonymous hedonic games and roommate games. They show that it is NP-hard to find a Pareto optimal solution both in anonymous and non-anonymous hedonic games, and provide an algorithm which determines a Pareto optimal solution for some of its variants, including roommate games, in polynomial time.…”

Section: Relation To the Literaturementioning

confidence: 99%

Stable and Pareto optimal group activity selection from ordinal preferences

Darmann

2018

Int J Game Theory

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In several situations agents need to be assigned to activities on basis of their preferences, and each agent can take part in at most one activity. Often, the preferences of the agents do not depend only on the activity itself but also on the number of participants in the respective activity. In the setting we consider, the agents hence have preferences over pairs "(activity, group size)" including the possibility "do nothing"; in this work, these preferences are assumed to be strict orders. The task will be to find stable assignments of agents to activities, for different concepts of stability such as Nash or core stability, and Pareto optimal assignments respectively. In this respect, particular focus is laid on two natural special cases of agents' preferences inherent in the considered model, namely increasing and decreasing preferences, where agents want to share an activity with as many (as few, respectively) agents as possible.

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“…Aziz et al [2016] proved that testing Pareto optimality is coNP-complete under additive preferences even if each agent is to be allocated two items. Aziz et al [2013] presented a general algorithm to compute and test Pareto optimal outcomes in discrete allocation and coalition formation settings with ordinal preferences. More recently, Damamme et al [2015] investigated the power of dynamics based on rational bilateral deals (swaps) in various settings including ours.…”

Section: Related Workmentioning

confidence: 99%

Publisher’s note

2017

Mathematical Social Sciences

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Pareto Optimality in Coalition Formation

Cited by 28 publications

References 12 publications

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Stable and Pareto optimal group activity selection from ordinal preferences

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