scholarly journals Two-sided Random Matching Markets: Ex-ante Equivalence of the Deferred Acceptance Procedures

2020 ◽  
Author(s):  
Simon Mauras
Keyword(s):  
Matching Markets ◽  
Random Matching ◽  
Ex Ante ◽  
Deferred Acceptance

scholarly journals Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures

2021 ◽  
Vol 9 (4) ◽  
pp. 1-14
Author(s):  
Simon Mauras
Keyword(s):  
Integral Formula ◽  
Combinatorial Problem ◽  
Stable Matching ◽  
Exclusion Principle ◽  
Matching Markets ◽  
Content Type ◽  
Ex Ante ◽  
Uniform Case ◽  
Deferred Acceptance ◽  
New Formula

Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal work by Gale and Shapley. When the input preference profile is generated from a distribution, we study the output distribution of two stable matching procedures: women-proposing-deferred-acceptance and men-proposing-deferred-acceptance. We show that the two procedures are ex-ante equivalent—that is, under certain conditions on the input distribution, their output distributions are identical. In terms of technical contributions, we generalize (to the non-uniform case) an integral formula, due to Knuth and Pittel, which gives the probability that a fixed matching is stable. Using an inclusion-exclusion principle on the set of rotations, we give a new formula that gives the probability that a fixed matching is the women/men-optimal stable matching.

The Limits of Incentives in Economic Matching Procedures

2020 ◽  
Author(s):  
Avinatan Hassidim ◽  
Assaf Romm ◽  
Ran I. Shorrer
Keyword(s):  
Private Information ◽  
Graduate Programs ◽  
Revenue Maximization ◽  
Matching Markets ◽  
Positive Signal ◽  
Best Interest ◽  
High Stakes ◽  
Field Evidence ◽  
Deferred Acceptance ◽  
Strategy Proof

Organizations often require agents’ private information to achieve critical goals such as efficiency or revenue maximization, but frequently it is not in the agents’ best interest to reveal this information. Strategy-proof mechanisms give agents incentives to truthfully report their private information. In the context of matching markets, they eliminate agents’ incentives to misrepresent their preferences. We present direct field evidence of preference misrepresentation under the strategy-proof deferred acceptance in a high-stakes matching environment. We show that applicants to graduate programs in psychology in Israel often report that they prefer to avoid receiving funding, even though the mechanism preserves privacy and funding comes with no strings attached and constitutes a positive signal of ability. Surveys indicate that other kinds of preference misrepresentation are also prevalent. Preference misrepresentation in the field is associated with weaker applicants. Our findings have important implications for practitioners designing matching procedures and for researchers who study them. This paper was accepted by Axel Ockenfels, decision analysis.

scholarly journals Expanding “Choice” in School Choice

2015 ◽  
Vol 7 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Yeon-Koo Che ◽  
Yosuke Yasuda
Keyword(s):  
Public Schools ◽  
School Choice ◽  
Ex Ante ◽  
Deferred Acceptance ◽  
School Preferences

Gale-Shapley's deferred acceptance (henceforth DA) mechanism has emerged as a prominent candidate for placing students to public schools. While DA has desirable fairness and incentive properties, it limits the applicants' abilities to communicate their preference intensities, which entails ex ante inefficiency when ties at school preferences are broken randomly. We propose a variant of deferred acceptance mechanism that allows students to influence how they are treated in ties. It inherits much of the desirable properties of DA but performs better in ex ante efficiency. (JEL D82, H75, I21, I28)

scholarly journals Erratum: “Unbalanced Random Matching Markets: The Stark Effect of Competition”

2020 ◽  
pp. 000-000
Author(s):  
Itai Ashlagi ◽  
Yash Kanoria ◽  
Jacob D. Leshno
Keyword(s):  
Stark Effect ◽  
Matching Markets ◽  
Random Matching

scholarly journals The Short-Side Advantage in Random Matching Markets

2022 ◽  
pp. 257-267
Author(s):  
Linda Cai ◽  
Clayton Thomas
Keyword(s):  
Matching Markets ◽  
Random Matching ◽  
Short Side

Resolving Conflicting Preferences in School Choice: The “Boston Mechanism” Reconsidered

2011 ◽  
Vol 101 (1) ◽  
pp. 399-410 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Yeon-Koo Che ◽  
Yosuke Yasuda
Keyword(s):  
School Choice ◽  
Ordinal Preferences ◽  
Boston Mechanism ◽  
Ex Ante ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Good Schools

Despite its widespread use, the Boston mechanism has been criticized for its poor incentive and welfare performances compared to the Gale-Shapley deferred acceptance algorithm (DA). By contrast, when students have the same ordinal preferences and schools have no priorities, we find that the Boston mechanism Pareto dominates the DA in ex ante welfare, that it may not harm but rather benefit participants who may not strategize well, and that, in the presence of school priorities, the Boston mechanism also tends to facilitate greater access than the DA to good schools for those lacking priorities at those schools. (JEL D82, I21, I28)

Unbalanced Random Matching Markets: The Stark Effect of Competition

2017 ◽  
Vol 125 (1) ◽  
pp. 69-98 ◽  
Author(s):  
Itai Ashlagi ◽  
Yash Kanoria ◽  
Jacob D. Leshno
Keyword(s):  
Stark Effect ◽  
Matching Markets ◽  
Random Matching
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