scholarly journals Strategic Performance of Deferred Acceptance in Dynamic Matching Problems

2019 ◽  
Vol 11 (2) ◽  
pp. 55-97 ◽  
Author(s):  
John Kennes ◽  
Daniel Monte ◽  
Norovsambuu Tumennasan
Keyword(s):  
School Choice ◽  
Computer Algorithm ◽  
Choice Problem ◽  
Strategic Performance ◽  
Matching Problems ◽  
Dynamic Matching ◽  
Deferred Acceptance

In dynamic matching problems, priorities often depend on previous allocations and create opportunities for manipulations that are absent in static problems. In the dynamic school choice problem, students can manipulate the period-by-period deferred acceptance (DA) mechanism. With a commonly used restriction on the schools’ priorities, manipulation vanishes as the number of agents increases, but without it the mechanism can be manipulated, even in large economies. We also check manipulation in large finite economies through a novel computer algorithm, which can check every possible manipulation by examining all the different matchings that a single player can induce. (JEL C78, I21, I28)

The Day Care Assignment: A Dynamic Matching Problem

2014 ◽  
Vol 6 (4) ◽  
pp. 362-406 ◽  
Author(s):  
John Kennes ◽  
Daniel Monte ◽  
Norovsambuu Tumennasan
Keyword(s):  
School Choice ◽  
Day Care ◽  
Student Mobility ◽  
Entry And Exit ◽  
Choice Problem ◽  
Matching Problem ◽  
Day Care Centers ◽  
Dynamic Matching ◽  
Strategy Proof ◽  
Pareto Efficient

We study the problem of centralized allocation of children to public day care centers, illustrated by the case of Denmark. Our framework applies to problems of dynamic matching in which there is entry and exit of agents over time; for example, the school choice problem once student mobility is taken into account. We show that there does not exist any mechanism that is both stable and strategy-proof. We also show that the well-known Top Trading Cycles mechanism is neither Pareto efficient nor strategy-proof. Finally, a mechanism in which parents sequentially choose menus of schools is both strategy-proof and Pareto efficient. (JEL C73, D82, I21)

Dynamic Matching in School Choice: Efficient Seat Reassignment After Late Cancellations

2020 ◽  
Vol 66 (11) ◽  
pp. 5341-5361
Author(s):  
Itai Feigenbaum ◽  
Yash Kanoria ◽  
Irene Lo ◽  
Jay Sethuraman
Keyword(s):  
High School ◽  
New York ◽  
New York City ◽  
School Choice ◽  
Operations Management ◽  
Natural Conditions ◽  
Dynamic Matching ◽  
On Demand ◽  
Deferred Acceptance ◽  
High School Admissions

In the school choice market, where scarce public school seats are assigned to students, a key operational issue is how to reassign seats that are vacated after an initial round of centralized assignment. Practical solutions to the reassignment problem must be simple to implement, truthful, and efficient while also alleviating costly student movement between schools. We propose and axiomatically justify a class of reassignment mechanisms, the permuted lottery deferred acceptance (PLDA) mechanisms. Our mechanisms generalize the commonly used deferred acceptance (DA) school choice mechanism to a two-round setting and retain its desirable incentive and efficiency properties. School choice systems typically run DA with a lottery number assigned to each student to break ties in school priorities. We show that under natural conditions on demand, the second-round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare and that reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms. Empirical investigations based on data from New York City high school admissions support our theoretical findings. This paper was accepted by Gad Allon, operations management.

scholarly journals Designing Random Allocation Mechanisms: Theory and Applications

2013 ◽  
Vol 103 (2) ◽  
pp. 585-623 ◽  
Author(s):  
Eric Budish ◽  
Yeon-Koo Che ◽  
Fuhito Kojima ◽  
Paul Milgrom
Keyword(s):  
Resource Allocation ◽  
School Choice ◽  
Real World ◽  
Random Allocation ◽  
Assignment Problems ◽  
Matching Problems ◽  
House Allocation ◽  
Controlled Choice ◽  
Ex Post ◽  
Ex Ante

Randomization is commonplace in everyday resource allocation. We generalize the theory of randomized assignment to accommodate multi-unit allocations and various real-world constraints, such as group-specific quotas (“controlled choice”) in school choice and house allocation, and scheduling and curriculum constraints in course allocation. We develop new mechanisms that are ex ante efficient and fair in these environments, and that incorporate certain non-additive substitutable preferences. We also develop a “utility guarantee” technique that limits ex post unfairness in random allocations, supplementing the ex ante fairness promoted by randomization. This can be applied to multi-unit assignment problems and certain two-sided matching problems. (JEL C78, D82)

scholarly journals Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

2019 ◽  
Vol 109 (4) ◽  
pp. 1486-1529 ◽  
Author(s):  
Gabrielle Fack ◽  
Julien Grenet ◽  
Yinghua He
Keyword(s):  
School Choice ◽  
Test Scores ◽  
Real Life ◽  
Truth Telling ◽  
Student Preferences ◽  
Ex Post ◽  
Is Strategy ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Novel Approaches

We propose novel approaches to estimating student preferences with data from matching mechanisms, especially the Gale-Shapley deferred acceptance. Even if the mechanism is strategy-proof, assuming that students truthfully rank schools in applications may be restrictive. We show that when students are ranked strictly by some ex ante known priority index (e.g., test scores), stability is a plausible and weaker assumption, implying that every student is matched with her favorite school/college among those she qualifies for ex post. The methods are illustrated in simulations and applied to school choice in Paris. We discuss when each approach is more appropriate in real-life settings. (JEL D11, D12, D82, I23)

scholarly journals Coalitions and cliques in the school choice problem

2015 ◽  
Vol 8 (5) ◽  
pp. 801-823
Author(s):  
Sinan Aksoy ◽  
Adam Azzam ◽  
Chaya Coppersmith ◽  
Julie Glass ◽  
Gizem Karaali ◽  
...  
Keyword(s):  
School Choice ◽  
Choice Problem

scholarly journals The structure of priority in the school choice problem

2019 ◽  
Vol 35 (3) ◽  
pp. 361-381
Author(s):  
Conal Duddy
Keyword(s):  
School Choice ◽  
Walking Distance ◽  
Extended Formulation ◽  
Choice Problem ◽  
A Priority ◽  
Priority Ordering

AbstractIn a school choice problem, each school has a priority ordering over the set of students. These orderings depend on criteria such as whether a student lives within walking distance or has a sibling at the school. A priority ordering provides a ranking of students but nothing more. I argue that this information is sufficient when priority is based on merit but not when priority is based on criteria such as walking distance. I propose an extended formulation of the problem wherein a ‘priority matrix’, indicating which criteria are satisfied by each student-school pair, replaces the usual priority orderings.

scholarly journals Heterogeneous Beliefs and School Choice Mechanisms

2020 ◽  
Vol 110 (5) ◽  
pp. 1274-1315 ◽  
Author(s):  
Adam J. Kapor ◽  
Christopher A. Neilson ◽  
Seth D. Zimmerman
Keyword(s):  
School Choice ◽  
Rational Expectations ◽  
Choice Behavior ◽  
Heterogeneous Beliefs ◽  
Welfare Costs ◽  
Subjective Beliefs ◽  
Opposite Conclusion ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)

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)

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