A unified approach to strategy-proofness of the deferred-acceptance rule and the top-trading cycles rule

2021 ◽  
Author(s):  
Hidekazu Anno ◽  
Sui Takahashi
Keyword(s):  
Unified Approach ◽  
Acceptance Rule ◽  
Top Trading Cycles ◽  
Deferred Acceptance ◽  
Strategy Proofness

scholarly journals Designing Matching Mechanisms under General Distributional Constraints

2017 ◽  
Vol 9 (2) ◽  
pp. 226-262 ◽  
Author(s):  
Masahiro Goto ◽  
Fuhito Kojima ◽  
Ryoji Kurata ◽  
Akihisa Tamura ◽  
Makoto Yokoo
Keyword(s):  
Distributional Constraints ◽  
Deferred Acceptance ◽  
Strategy Proofness

To handle various applications, we study matching under constraints. The only requirement on the constraints is heredity; given a feasible matching, any matching with fewer students at each school is also feasible. Heredity subsumes existing constraints such as regional maximum quotas and diversity constraints. With constraints, there may not exist a matching that satisfies fairness and nonwastefulness (i.e., stability). We demonstrate our new mechanism, the Adaptive Deferred Acceptance mechanism (ADA), satisfies strategy-proofness for students, nonwastefulness, and a weaker fairness property. We also offer a technique to apply ADA even if heredity is violated (e.g., minimum quotas). (JEL C78, D47, D63, D82, I20)

The Cutoff Structure of Top Trading Cycles in School Choice

2020 ◽  
Author(s):  
Jacob D Leshno ◽  
Irene Lo
Keyword(s):  
School Choice ◽  
School Quality ◽  
Competitive Equilibrium ◽  
Optimal Investment ◽  
Comparative Statics ◽  
Closed Form Solutions ◽  
Top Trading Cycles ◽  
Deferred Acceptance

Abstract This paper develops a tractable theoretical framework for the Top Trading Cycles (TTC) mechanism for school choice that allows quantifying welfare and optimizing policy decisions. We compute welfare for TTC and Deferred Acceptance (DA) under different priority structures, and find that the choice of priorities can have larger welfare implications than the choice of mechanism. We solve for the welfare-maximizing distributions of school quality for parametrized economies, and find that optimal investment decisions can be very different under TTC and DA. Our framework relies on a novel characterization of the TTC assignment in terms of a cutoff for each pair of schools. These cutoffs parallel prices in competitive equilibrium, with students’ priorities serving the role of endowments. We show that these cutoffs can be computed directly from the distribution of preferences and priorities in a continuum model, and derive closed-form solutions and comparative statics for parameterized settings. The TTC cutoffs clarify the role of priorities in determining the TTC assignment, but also demonstrate that TTC is more complicated than DA.

scholarly journals Robust group strategy‐proofness

2021 ◽  
Vol 16 (4) ◽  
pp. 1351-1389
Author(s):  
Steven Kivinen ◽  
Norovsambuu Tumennasan
Keyword(s):  
Private Information ◽  
Truth Telling ◽  
Private Goods ◽  
Group Strategy ◽  
Free Disposal ◽  
Ex Post ◽  
Indivisible Objects ◽  
Social Choice Functions ◽  
Deferred Acceptance ◽  
Strategy Proofness

Strategy‐proofness (SP) is a sought‐after property in social choice functions because it ensures that agents have no incentive to misrepresent their private information at both the interim and ex post stages. Group strategy‐proofness (GSP), however, is a notion that is applied to the ex post stage but not to the interim stage. Thus, we propose a new notion of GSP, coined robust group strategy‐proofness (RGSP), which ensures that no group benefits by deviating from truth telling at the interim stage. We show for the provision of a public good that the Minimum Demand rule (Serizawa (1999)) satisfies RGSP when the production possibilities set satisfies a particular topological property. In the problem of allocating indivisible objects, an acyclicity condition on the priorities is both necessary and sufficient for the Deferred Acceptance rule to satisfy RGSP, but is only necessary for the Top Trading Cycles rule. For the allocation of divisible private goods among agents with single‐peaked preferences (Sprumont (1991)), only free disposal, group replacement monotonic rules within the class of sequential allotment rules satisfy RGSP.

scholarly journals Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match

2009 ◽  
Vol 99 (5) ◽  
pp. 1954-1978 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Parag A. Pathak ◽  
Alvin E. Roth
Keyword(s):  
High School ◽  
New York ◽  
New York City ◽  
Field Data ◽  
Open Questions ◽  
Trade Offs ◽  
Deferred Acceptance ◽  
School Preferences ◽  
Potential Efficiency ◽  
Strategy Proofness

The design of the New York City (NYC) high school match involved trade-offs among efficiency, stability, and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences—ties—in school preferences. Simulations with field data and the theory favor breaking indifferences the same way at every school—single tiebreaking—in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tiebreaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions. (JEL C78, D82, I21)

A Unified Approach to Study the Thermal Dynamics in Multilongitudinal Mode Semiconductor Lasers

2001 ◽  
Vol 20 (2) ◽  
pp. 159-169 ◽  
Author(s):  
M. Ganesh Madhan ◽  
P. R. Vaya ◽  
N. Gunasekaran
Keyword(s):  
Semiconductor Lasers ◽  
Unified Approach ◽  
Thermal Dynamics
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