Nash Implementation of Matching Rules

Kara, Tarık; Sönmez, Tayfun

doi:10.1006/jeth.1996.0024

Cited by 65 publications

(27 citation statements)

References 19 publications

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“…The example also shows that deferred acceptance rules do not always satisfy Maskin monotonicity (cf. Kara and Sönmez (1996)) and that some top trading cycle rules violate IR monotonicity, but satisfy Maskin monotonicity. EXAMPLE 1: Let N = {i j k} O = {a b}, and q a = q b = 1.…”

Section: First Characterization Of Deferred Acceptance Rulesmentioning

confidence: 99%

Axioms for Deferred Acceptance

Kojima

Manea

2010

Econometrica

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The deferred acceptance algorithm is often used to allocate indivisible objects when monetary transfers are not allowed. We provide two characterizations of agentproposing deferred acceptance allocation rules. Two new axioms-individually rational monotonicity and weak Maskin monotonicity-are essential to our analysis. An allocation rule is the agent-proposing deferred acceptance rule for some acceptant substitutable priority if and only if it satisfies non-wastefulness and individually rational monotonicity. An alternative characterization is in terms of non-wastefulness, population monotonicity, and weak Maskin monotonicity. We also offer an axiomatization of the deferred acceptance rule generated by an exogenously specified priority structure. We apply our results to characterize efficient deferred acceptance rules.

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Section: First Characterization Of Deferred Acceptance Rulesmentioning

confidence: 99%

Axioms for Deferred Acceptance

Kojima

Manea

2010

Econometrica

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“…We use the concept of full implementation, meaning that any stable matching is achievable (in Nash equilibrium) by letting agents act strategically. Given weakly responsive preferences, one straightforward idea to approach the problem is to first decompose any couples market into an associated singles market and then to apply previously established implementation results for singles market (e.g., Kara and Sönmez, 1996). However, as argued above, the stable correspondence of the associated singles markets and the stable correspondence for couples markets are not logically related.…”

Section: Matching With Couples Stability and Responsive Preferencesmentioning

confidence: 99%

“…One may be tempted to think that Theorem 2 for the weakly responsive preferences domain can be proved by considering an associated singles market, applying previous results on monotonicity of the stable correspondence (e.g., Kara and Sönmez, 1996) in such markets, and then transferring the result back to the original couples market. However, there are two main problems with this "proof strategy".…”

Section: Monotonicity and Nash Implementationmentioning

confidence: 99%

Stability and Nash implementation in matching markets with couples

Haake

Klaus²

2008

Theory Decis

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We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable. JEL classification: C62, C78, D78, J41.

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“…It should be noted that the proof of Tadenuma and Toda (1998) cannot be adapted for the theorems in the present paper because it uses transformations of preferences that are not rank-enhancements of partners. Kara and Sönmez (1996) showed that no proper subcorrespondence of the stable matchings correspondence is Maskin monotonic. But their proof relies crucially on the preference orders in which being unmatched is not necessarily worst for the agents.…”

Section: Introductionmentioning

confidence: 99%

Partnership-enhancement and stability in matching problems

Tadenuma

2012

Rev Econ Design

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In two-sided matching problems, we consider "natural" changes in preferences of agents in which only the rankings of current partners are enhanced.We introduce two desirable properties of matching rules under such rankenhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the "irrelevant" agents, whose preferences as well as whose original partners' preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.

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Nash Implementation of Matching Rules

Cited by 65 publications

References 19 publications

Axioms for Deferred Acceptance

Axioms for Deferred Acceptance

Stability and Nash implementation in matching markets with couples

Partnership-enhancement and stability in matching problems

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