Matching with slot-specific priorities: Theory

Kominers, Scott Duke; Sönmez, Tayfun

doi:10.3982/te1839

Cited by 132 publications

(104 citation statements)

References 44 publications

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“…In the case of slot-specific priorities, Sönmez (2013, 2014) show that the rule induced by the cumulative offer process is both stable and strategy-proof. The uniqueness follows from Theorem 1.…”

Section: Corollary 1 Suppose That Every Hospital H ∈ H Has a Choice mentioning

confidence: 99%

“…In the case of slot-specific priorities, Kominers and Sönmez (2014) show that the cumulative offer process may not choose the doctor-optimal stable allocation even when it exists (Example 4), whereas it always induces a stable and strategy-proof rule (Theorem 4).…”

Section: Fact 1 the Doctor-optimal Stable Rule Can Be Strategy-proofmentioning

confidence: 99%

“…Fact 2 (Kominers and Sönmez, 2014). A stable and strategy-proof rule may choose an allocation that is strictly dominated by another stable allocation.…”

Section: Fact 1 the Doctor-optimal Stable Rule Can Be Strategy-proofmentioning

confidence: 99%

“…Sönmez (2013, 2014) Definition 6. Given (C H (·), D ), the cumulative offer process proceeds as follows.…”

Section: Definition 1 Hospital H's Choice Function Satisfies the Submentioning

confidence: 99%

“…1 With those conditions, Sakai (2011) also generalizes the uniqueness result and hence, the study of stable and strategy-proof rules is necessarily the study of the deferred acceptance. At the same time, however, the rapid developments of the matching with contracts literature has started to cover, in both theory and practice, the cases that violate those pre-known conditions for the deferred acceptance to be stable and/or strategy-proof (e.g., Dimakopoulos and Heller, 2014;Hatfield and Kojima, 2010;Sönmez, 2013, 2014).…”

mentioning

confidence: 99%

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On Stable and Strategy-Proof Rules in Matching Markets with Contracts

Hirata

Kasuya

2015

SSRN Journal

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This paper studies stable and (one-sided) strategy-proof matching rules in manyto-one matching markets with contracts. First, the number of such rules is shown to be at most one. Second, the doctor-optimal stable rule, whenever it exists, is shown to be the unique candidate for a stable and strategy-proof rule. Third, a stable and strategyproof rule, when exists, is shown to be second-best optimal for doctor welfare, in the sense that no individually-rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Notably, all those results are established without any substitutes conditions on hospitals' choice functions, and hence, the proofs do not rely on the "rural hospital" theorem. We also show by example that the outcomes of a stable and strategy-proof rule do not always coincide with those of the cumulative offer process; hence, the above results hold not because the cumulative offer process is the only candidate for stable and strategyproof rules.

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Section: Corollary 1 Suppose That Every Hospital H ∈ H Has a Choice mentioning

confidence: 99%

Section: Fact 1 the Doctor-optimal Stable Rule Can Be Strategy-proofmentioning

confidence: 99%

“…Fact 2 (Kominers and Sönmez, 2014). A stable and strategy-proof rule may choose an allocation that is strictly dominated by another stable allocation.…”

Section: Fact 1 the Doctor-optimal Stable Rule Can Be Strategy-proofmentioning

confidence: 99%

“…Sönmez (2013, 2014) Definition 6. Given (C H (·), D ), the cumulative offer process proceeds as follows.…”

Section: Definition 1 Hospital H's Choice Function Satisfies the Submentioning

confidence: 99%

mentioning

confidence: 99%

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On Stable and Strategy-Proof Rules in Matching Markets with Contracts

Hirata

Kasuya

2015

SSRN Journal

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Stable Marriage with Covering Constraints–A Complete Computational Trichotomy

Mnich

Schlotter

2017

Algorithmic Game Theory

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We consider Stable Marriage with Covering Constraints (SMC): in this variant of Stable Marriage, we distinguish a subset of women as well as a subset of men, and we seek a matching with fewest number of blocking pairs that matches all of the distinguished people. We investigate how a set of natural parameters, namely the maximum length of preference lists for men and women, the number of distinguished men and women, and the number of blocking pairs allowed determine the computational tractability of this problem. Our main result is a complete complexity trichotomy that, for each choice of the studied parameters, classifies SMC as polynomial-time solvable, NP-hard and fixed-parameter tractable, or NP-hard and W[1]-hard. We also classify all cases of one-sided constraints where only women may be distinguished.

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