Stability of marriage with externalities

Hafalır, İsa Emin

doi:10.1007/s00182-008-0122-9

Cited by 65 publications

(31 citation statements)

References 7 publications

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“…Consequently, most research has focused on identifying when stable matchings do and do not exist. Some papers have proceeded by constraining the matching problem through restrictions of the possible preference orderings, [3,7,11,12,15,17], while others have considered variations on the standard notion of stability [1,4,23]. Our paper also considers a restriction of the model which allows us to more easily characterize the class of stable matchings.…”

Section: Introductionmentioning

confidence: 99%

Peer Effects and Stability in Matching Markets

Bodine-Baron

Lee

Chong

et al. 2011

Lecture Notes in Computer Science

200

121

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Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In the these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings.In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. Our model captures peer effects and complementarities using utility functions rather than traditional preference ordering. With this model and considering pairwise stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a stable matching. To asses the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we prove general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

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Section: Introductionmentioning

confidence: 99%

Peer Effects and Stability in Matching Markets

Bodine-Baron

Lee

Chong

et al. 2011

Lecture Notes in Computer Science

200

121

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“…Hafalir [27] takes a different approach centered around the negativity result of Theorem 2.3. The trick behind the negativity result of Theorem 2.3 is that for a given profile of estimation functions for each i ∈ M ∪ W , we can construct preferences such that φ-stable matchings do not exist without arguing whether estimations were sound based on the preferences at hand.…”

Section: An Extension Of the One-to-one Model Using Estimation Functionsmentioning

confidence: 99%

“…The trick behind the negativity result of Theorem 2.3 is that for a given profile of estimation functions for each i ∈ M ∪ W , we can construct preferences such that φ-stable matchings do not exist without arguing whether estimations were sound based on the preferences at hand. Hafalir [27] first limits the estimation functions that can be construed based on the preferences of the agents. In this sense, estimation functions are endogenously given.…”

Section: An Extension Of the One-to-one Model Using Estimation Functionsmentioning

confidence: 99%

“…In this sense, estimation functions are endogenously given. Hafalir [27] then defines what are called sophisticated estimation functions and shows that these estimation functions can circumvent the negative result of Sasaki and Toda [62]. These estimation functions, like those of Li [40], are defined inductively.…”

Section: An Extension Of the One-to-one Model Using Estimation Functionsmentioning

confidence: 99%

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Two-Sided Matching With Externalities: A Survey

Bando

Kawasaki

Muto

2016

JORSJ

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The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.

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“…7 In fact, our main comparative statics result is new even in the setting without externalities as is our synthesis of classical and far-sighted stability. 8 The rich subsequent literature, e.g., Chowdhury (2004);Hafalir (2008); Eriksson, Jansson, and Vetander (2011);Chen (2013); Gudmundsson and Habis (2013); Salgado-Torres (2011a,b)-maintained the focus on the existence question while refining Sasaki and Toda's weak stability concept by varying the degree to which the rematches of other agents penalize the blocking pair. Bodine-Baron, Lee, Chong, Hassibi, and Wierman (2011) analyze a related weak stability concept in a setting with peer effects.…”

mentioning

confidence: 99%

Matching with Externalities

Pycia

Yenmez

2014

SSRN Journal

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We incorporate externalities into the stable matching theory of two-sided markets. Extending the classical substitutes condition to allow for externalities, we establish that stable matchings exist when agent choices satisfy substitutability. In addition, we show that the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, remain valid despite the presence of externalities even though the standard fixed-point techniques do not apply. Furthermore, we establish novel comparative statics on externalities.

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Stability of marriage with externalities

Cited by 65 publications

References 7 publications

Peer Effects and Stability in Matching Markets

Peer Effects and Stability in Matching Markets

Two-Sided Matching With Externalities: A Survey

Matching with Externalities

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