Stable Marriage with General Preferences

Farczadi, Linda; Georgiou, Konstantinos; Könemann, Jochen

doi:10.1007/s00224-016-9687-z

Cited by 13 publications

(27 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some notable mentions out of those lists are Shapely and Shubik [28], X. Deng et al [12], Granot et al [16], X. Deng and Q. Fang [11], Chalkiadakis et al [8], etc. Farczadi et al [14] extended the results of the Kleinberg-Tardos model for networks with agents with general capacities. Hajiaghayi et al [18] also did the work in that line.…”

Section: Previous Workmentioning

confidence: 98%

See 1 more Smart Citation

Stability concepts in bargaining games

Kundu¹

2021

Preprint

View full text Add to dashboard Cite

In this thesis we discuss some novel concepts of stability in bargaining games, over a network setting. So far, the studies on bargaining games were done as profit sharing problems, whose underlying combinatorial optimization problems are of packing type. In our work, we study bargaining games from a cost sharing perspective, where the underlying combinatorial optimization problems are covering type problems. Unlike previous studies, where bargaining processes are restricted to only two players, we study bargaining games over a more generic hypergraph setting, which allows any bargaining process to be formed among any number of players. In previous studies of bargaining games, the objects that are being negotiated are assumed to be uniform and only the outcomes of the negotiations are allowed to be different. However, in our study, we accommodate possibilities of non-uniform weights of the objects that are being negotiated, which is closer to any real life scenario. Finally we extend our study to incorporate socially aware players by introducing a relaxed and innovative definition of stability.

show abstract

Section: Previous Workmentioning

confidence: 98%

“…In our work we build on top of the study of Kleinberg and Tardos [21], Bateni et al [2] and Farczadi et al [14]. The common thread between their work and ours is the study of stability over a network bargaining game.…”

Section: Our Contributionmentioning

confidence: 99%

Stability concepts in bargaining games

Kundu¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…They also considered the case of certain, but cyclic preferences and showed that deciding whether a weakly stable matching exists is NP-complete if both sides can have cycles in their preferences. Strongly and super stable matchings were discussed by Farczadi et al [11]. Throughout their paper they assumed that one side has strict preferences, and proved that finding a strongly or a super stable matching (or proving that none exists) can be done in polynomial time if the other side has cyclic lists, where cycles of length at least 3 are permitted to occur, but the problems become NP-complete as soon as cycles of length 2 are also allowed.…”

Section: Related Workmentioning

confidence: 99%

“…While it would lead to an equally correct model, we chose incomparability over being equally good consciously. Some early papers [19,20] do not distinguish between two agents being incomparable and equally good, while some others in the more recent literature [3,11] motivate strong and super-stability with uncertain information. Our definition fits the more recent framework.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Pairwise Preferences in the Stable Marriage Problem

Cseh

Juhos

2021

ACM Trans. Econ. Comput.

View full text Add to dashboard Cite

We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges, and they also have the right to declare a draw or even withdraw from such a comparison. This freedom is then gradually restricted as we specify six stages of orderedness in the preferences, ending with the classical case of strictly ordered lists. We study all cases occurring when combining the three known notions of stability—weak, strong, and super-stability—under the assumption that each side of the bipartite market obtains one of the six degrees of orderedness. By designing three polynomial algorithms and two NP-completeness proofs, we determine the complexity of all cases not yet known and thus give an exact boundary in terms of preference structure between tractable and intractable cases.

show abstract

On the Existence of Three-Dimensional Stable Matchings with Cyclic Preferences

Lam

Plaxton

2019

Algorithmic Game Theory

View full text Add to dashboard Cite

We study the three-dimensional stable matching problem with cyclic preferences. This model involves three types of agents, with an equal number of agents of each type. The types form a cyclic order such that each agent has a complete preference list over the agents of the next type. We consider the open problem of the existence of three-dimensional matchings in which no triple of agents prefer each other to their partners. Such matchings are said to be weakly stable. We show that contrary to published conjectures, weakly stable three-dimensional matchings need not exist. Furthermore, we show that it is NP-complete to determine whether a weakly stable three-dimensional matchings exists. We achieve this by reducing from the variant of the problem where preference lists are allowed to be incomplete. Our results can be generalized to the k-dimensional stable matching problem with cyclic preferences for k ≥ 3.

show abstract

Stable Marriage with General Preferences

Cited by 13 publications

References 24 publications

Stability concepts in bargaining games

Stability concepts in bargaining games

Pairwise Preferences in the Stable Marriage Problem

On the Existence of Three-Dimensional Stable Matchings with Cyclic Preferences

Contact Info

Product

Resources

About