Hedonic Games with Fixed-Size Coalitions

Bilò, Vittorio; Monaco, Gianpiero; Moscardelli, Luca

doi:10.1609/aaai.v36i9.21156

Cited by 11 publications

(8 citation statements)

References 28 publications

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“…It should be noted that Lemmas 2 and 3 also contrast many other models where outputs maximizing social welfare are stable for symmetric utilities [11,6,15].…”

Section: Structural Properties Of Outcomesmentioning

confidence: 97%

Maximizing Social Welfare in Score-Based Social Distance Games

Ganian¹,

Hamm²,

Knop³

et al. 2023

Electron. Proc. Theor. Comput. Sci.

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Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u s depends on a generic scoring vector s, which may be customized to match the specifics of each individual application scenario.As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u s . We provide more efficient algorithms when dealing with specific choices of u s or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.

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“…It should be noted that Lemmas 2 and 3 also contrast many other models where outputs maximizing social welfare are stable for symmetric utilities [11,6,15].…”

Section: Structural Properties Of Outcomesmentioning

confidence: 97%

Maximizing Social Welfare in Score-Based Social Distance Games

Ganian¹,

Hamm²,

Knop³

et al. 2023

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

show abstract

“…In addition, a recent series of work considers deviation dynamics for hedonic games, which constitute another time-dependent model of coalition formation (see, e.g., Bilò et al 2018;Brandt, Bullinger, and Wilczynski 2023;Carosi, Monaco, and Moscardelli 2019). In particular, ASHGs and close variants are studied in depth (Bilò, Monaco, and Moscardelli 2022;Boehmer, Bullinger, and Kerkmann 2023;Brandt, Bullinger, and Tappe 2022;Bullinger and Suksompong 2023).…”

Section: Related Workmentioning

confidence: 99%

Stability in Online Coalition Formation

Bullinger,

Romen

2024

AAAI

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Coalition formation is concerned with the question of how to partition a set of agents into disjoint coalitions according to their preferences. Deviating from most of the previous work, we consider an online variant of the problem, where agents arrive in sequence and whenever an agent arrives, they have to be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on the objective of maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve stable coalition structures in an online setting, and focus on stability concepts based on deviations by single agents. We present a comprehensive picture in additively separable hedonic games, leading to dichotomies, where positive results are obtained by deterministic algorithms and negative results even hold for randomized algorithms.

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“…Our work can be viewed as a hedonic game with symmetric, binary, and additively separable preferences, and with the restriction that the partition produced have exactly k almost equal-sized parts. Hedonic games with restrictions on the number of groups have been studied before, but under other objectives, such as swap stability (Bilò, Monaco, and Moscardelli 2022), Pareto optimality (Cseh, Fleiner, and Harján 2019). Moreover, Sless et al (2018) consider a strictly weaker version of the core, without the size constraint, for which they provide positive results that do not carry over our imbalanced case.…”

Section: Related Workmentioning

confidence: 99%

Partitioning Friends Fairly

Micha

Nikolov

et al. 2023

AAAI

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We consider the problem of partitioning n agents in an undirected social network into k almost equal in size (differing by at most one) groups, where the utility of an agent for a group is the number of her neighbors in the group. The core and envy-freeness are two compelling axiomatic fairness guarantees in such settings. The former demands that there be no coalition of agents such that each agent in the coalition has more utility for that coalition than for her own group, while the latter demands that no agent envy another agent for the group they are in. We provide (often tight) approximations to both fairness guarantees, and many of our positive results are obtained via efficient algorithms.

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Hedonic Games with Fixed-Size Coalitions

Cited by 11 publications

References 28 publications

Maximizing Social Welfare in Score-Based Social Distance Games

Maximizing Social Welfare in Score-Based Social Distance Games

Stability in Online Coalition Formation

Partitioning Friends Fairly

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