Review of Direct Matching Markets and the Deferred Acceptance Algorithm

2012 ◽  
Author(s):  
Serge L. Wind
Keyword(s):  
Matching Markets ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance

scholarly journals Stability in Matching Markets with Complex Constraints

2021 ◽  
Author(s):  
Hai Nguyen ◽  
Thành Nguyen ◽  
Alexander Teytelboym
Keyword(s):  
Refugee Resettlement ◽  
The Novel ◽  
Matching Markets ◽  
Constraint Violation ◽  
Constraint Matrix ◽  
Knapsack Constraints ◽  
Multidimensional Knapsack ◽  
Practical Constraint ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance

We develop a model of many-to-one matching markets in which agents with multiunit demand aim to maximize a cardinal linear objective subject to multidimensional knapsack constraints. The choice functions of agents with multiunit demand are therefore not substitutable. As a result, pairwise stable matchings may not exist and even when they do, may be highly inefficient. We provide an algorithm that finds a group-stable matching that approximately satisfies all the multidimensional knapsack constraints. The novel ingredient in our algorithm is a combination of matching with contracts and Scarf’s Lemma. We show that the degree of the constraint violation under our algorithm is proportional to the sparsity of the constraint matrix. The algorithm, therefore, provides practical constraint violation bounds for applications in contexts, such as refugee resettlement, day care allocation, and college admissions with diversity requirements. Simulations using refugee resettlement data show that our approach produces outcomes that are not only more stable, but also more efficient than the outcomes of the Deferred Acceptance algorithm. Moreover, simulations suggest that in practice, constraint violations under our algorithm would be even smaller than the theoretical bounds. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Choice and Matching

2017 ◽  
Vol 9 (3) ◽  
pp. 126-147 ◽  
Author(s):  
Christopher P. Chambers ◽  
M. Bumin Yenmez
Keyword(s):  
The Other ◽  
Matching Theory ◽  
Matching Markets ◽  
Powerful Technique ◽  
Static Result ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance

We study path-independent choice rules applied to a matching context. We use a classic representation of these choice rules to introduce a powerful technique for matching theory. Using this technique, we provide a deferred acceptance algorithm for many-to-many matching markets with contracts and study its properties. Next, we obtain a compelling comparative static result: if one agent's choice expands, the remaining agents on her side of the market are made worse off, while agents on the other side of the market are made better off. Finally, we establish several results related to path-independent choice rules. (JEL C78, D11, D71, D86)

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.

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