Substitutes and stability for matching with contracts

Hatfield, John William; Kojima, Fuhito

doi:10.1016/j.jet.2010.01.007

Cited by 176 publications

(126 citation statements)

References 38 publications

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“…. ., we update these sets and matchings 25 The tracking of reference matchings has no counterpart in earlier formulations of the deferred acceptance algorithms of, among many others, Gale and Shapley (1962), Roth (1984), Adachi (2000), Fleiner (2003), Echenique and Oviedo (2004), Hatfield and Milgrom (2005), Echenique and Oviedo (2006), Echenique and Yenmez (2007), Ostrovsky (2008), Kojima (2010), andBando (2014). In these papers, there is no need to track reference matchings and the deferred acceptance algorithm terminates when there are no more rejections and no new offers.…”

Section: Stable Matchingsmentioning

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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Section: Stable Matchingsmentioning

confidence: 99%

Matching with Externalities

Pycia

Yenmez

2014

SSRN Journal

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“…For any branch b, we construct the adjusted priorities π + b as described above. 13 Throughout the paper we will assume that λq b and (1 − λ)q b as are integer values for any branch b. This is for expositional simplicity and has no impact on the analysis.…”

Section: The Usma Mechanismmentioning

confidence: 99%

Matching With (Branch-of-Choice) Contracts at the United States Military Academy

2013

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Branch selection is a key decision in a cadet's military career. Cadets at USMA can increase their branch priorities at a fraction of slots by extending their service agreement. This real-life matching problem fills an important gap in market design literature.Although priorities fail a key substitutes condition, the agent-optimal stable mechanism is well-defined, and in contrast to the current USMA mechanism it is fair, stable, and strategy-proof. Adoption of this mechanism benefits cadets and the Army. This new application shows that matching with contracts model is practically relevant beyond traditional domains that satisfy the substitutes condition. JEL Classification Numbers: C78, D63, D78

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“…We are also interested in the relation between unilateral substitutability introduced by Hatfield and Kojima (2010) and substitutable completability. Hatfield et al show that unilateral substitutability is a special case of observable substitutability.…”

Section: Introductionmentioning

confidence: 99%

“…In the graph "condition a → condition b" means that condition a implies condition b. Hatfield and Kojima (2010) Unilateral substitutability & IRC Kadam (2014) this paper In Section 2 we define the standard many-to-one matching with contracts model. In Section 3 we define weakly observable substitutability and weakly observable substitutability across workers and prove that they are sufficient conditions.…”

Section: Introductionmentioning

confidence: 99%

On sufficient conditions for the existence of stable matchings with contracts

Zhang

2016

Economics Letters

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We introduce two new sufficient conditions for the existence of stable outcomes in many-to-one matching with contracts. The conditions subsume the observable substitutability of Hatfield et al. (2015) and the substitutable completability of Hatfield and Kominers (2016) as special cases. We also prove that unilaterally substitutability and irrelevance of rejected contracts imply substitutable completability. Echenique for guidance, and the editor and an anonymous referee for comments. All errors are mine.

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Substitutes and stability for matching with contracts

Cited by 176 publications

References 38 publications

Matching with Externalities

Matching with Externalities

Matching With (Branch-of-Choice) Contracts at the United States Military Academy

On sufficient conditions for the existence of stable matchings with contracts

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