scholarly journals Strategic Issues in One-to-One Matching with Externalities

2020 ◽  
pp. 2050015
Author(s):  
Ayşe Mumcu ◽  
Ismail Saglam
Keyword(s):  
Impossibility Result ◽  
Stable Matching ◽  
Matching Problem ◽  
Men And Women ◽  
Strategic Issues ◽  
Stable Mechanism ◽  
Is Strategy ◽  
Strategy Proof ◽  
One To One ◽  
Appl Math

We consider strategic issues in one-to-one matching with externalities. We show that no core (stable) mechanism is strategy-proof, extending an impossibility result of [Roth, A. E. [1982] The economics of matching: Stability and incentives, Math. Oper. Res. 7(4), 617–628] obtained in the absence of externalities. Moreover, we show that there are no limits on successful manipulation of preferences by coalitions of men and women, in contrast with the result of [Demange, G., Gale, D. and Sotomayor, M. [1987] A further note on the stable matching problem, Discrete Appl. Math. 16(3), 217–222] obtained in the absence of externalities.

scholarly journals Matching with floor constraints

2021 ◽  
Vol 16 (3) ◽  
pp. 911-942
Author(s):  
Sumeyra Akin
Keyword(s):  
Additional Condition ◽  
Stable Matching ◽  
Medical Residency ◽  
Matching Markets ◽  
Prominent Feature ◽  
Stable Matchings ◽  
Teacher Assignment ◽  
Is Strategy ◽  
Strategy Proof ◽  
Hard Floor

Floor constraints are a prominent feature of many matching markets, such as medical residency, teacher assignment, and military cadet matching. We develop a theory of matching markets under floor constraints. We introduce a stability notion, which we call floor respecting stability, for markets in which (hard) floor constraints must be respected. A matching is floor respecting stable if there is no coalition of doctors and hospitals that can propose an alternative matching that is feasible and an improvement for its members. Our stability notion imposes the additional condition that a coalition cannot reassign a doctor outside the coalition to another hospital (although she can be fired). This condition is necessary to guarantee the existence of stable matchings. We provide a mechanism that is strategy‐proof for doctors and implements a floor respecting stable matching.

Sequential Preference Revelation in Incomplete Information Settings

2021 ◽  
Vol 13 (1) ◽  
pp. 116-147
Author(s):  
James Schummer ◽  
Rodrigo A. Velez
Keyword(s):  
Incomplete Information ◽  
Real World ◽  
Private Information ◽  
Allocation Rules ◽  
Is Strategy ◽  
Strategy Proof ◽  
Simultaneous Move

Strategy-proof allocation rules incentivize truthfulness in simultaneous move games, but real world mechanisms sometimes elicit preferences sequentially. Surprisingly, even when the underlying rule is strategy-proof and nonbossy, sequential elicitation can yield equilibria where agents have a strict incentive to be untruthful. This occurs only under incomplete information, when an agent anticipates that truthful reporting would signal false private information about others’ preferences. We provide conditions ruling out this phenomenon, guaranteeing all equilibrium outcomes to be welfare-equivalent to truthful ones. (JEL C73, D45, D82, D83)

Near-Feasible Stable Matchings with Couples

2018 ◽  
Vol 108 (11) ◽  
pp. 3154-3169 ◽  
Author(s):  
Thành Nguyen ◽  
Rakesh Vohra
Keyword(s):  
Medical Students ◽  
Stable Matching ◽  
Teaching Hospitals ◽  
Matching Problem ◽  
Stable Matchings ◽  
Student Preferences

The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a “nearby” instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two. (JEL C78, D47, I11, J41, J44)

scholarly journals Efficient Parameterized Word Matching Using Bit-Parallelism and Partitioning the Text

2016 ◽  
Vol 2 (2) ◽  
pp. 20
Author(s):  
Rajesh Prasad
Keyword(s):  
Experimental Results ◽  
Brute Force ◽  
White Space ◽  
Matching Problem ◽  
One To One ◽  
Brute Force Approach ◽  
Better Than

Word matching problem is to find all the exact occurrences of a pattern P[0...m-1] in the text T[0...n-1], where P neither contains any white space nor preceded and followed by space. In the parameterized word matching problem, a given word P[0...m-1] is said to match with a sub-word t of the text T[0...n-1], if there exists a one-to-one correspondence between the symbols of P and the symbols of t. Exact Word Matching (EWM) problem has been previously solved by partitioning the text into number of tables in the pre-processing phase and then applying either brute force approach or fast hashing during the searching process. This paper presents an extension of EWM problem for parameterized word matching. It first split the text into number of tables in the pre-processing phase and then applying prev-encoding and bit-parallelism technique, Parameterized Shift-Or (PSO) during the searching phase. Experimental results show that this technique performs better than PSO.

Large Electorates

2011 ◽  
Author(s):  
Michel Balinski ◽  
Rida Laraki
Keyword(s):  
Ordered Set ◽  
Common Language ◽  
Is Strategy ◽  
Strategy Proof

This chapter emphasizes the simplification of majority-ranking, stating that an increased number of judges in the jury or voters in an electorate or use of simplified common language help to simplify majority-values of competitors or candidates. Ordered set grades help obtain majority-value by beginning with the majority-grade or the lower middlemost grade and following alternating grades. Unambiguous order among the competitors can be determined with certainty given an increased number of judges or voters and relatively few grades. The competitor’s majority-gauge, which is strategy-proof-in-grading, is explained with the help of a theorem. Upper, lower, and difference tie-breaking rules that are strategy-proof-in-grading share properties with the majority-gauge-ranking.

scholarly journals On the Approximability of the Stable Matching Problem with Ties of Size Two

Algorithmica ◽  
2020 ◽  
Vol 82 (9) ◽  
pp. 2668-2686
Author(s):  
Robert Chiang ◽  
Kanstantsin Pashkovich
Keyword(s):  
Stable Matching ◽  
Matching Problem

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 Two-Sided Matching with Endogenous Preferences

2015 ◽  
Vol 7 (3) ◽  
pp. 241-258 ◽  
Author(s):  
Yair Antler
Keyword(s):  
Stable Matching ◽  
The Other ◽  
Matching Theory ◽  
Endogenous Preferences ◽  
Matching Problem ◽  
Matching Mechanism

We modify the stable matching problem by allowing agents' preferences to depend on the endogenous actions of agents on the other side of the market. Conventional matching theory results break down in the modified setup. In particular, every game that is induced by a stable matching mechanism (e.g., the Gale-Shapley mechanism) may have equilibria that result in matchings that are not stable with respect to the agents' endogenous preferences. However, when the Gale-Shapley mechanism is slightly modified, every equilibrium of its induced game results in a pairwise stable matching with respect to the endogenous preferences as long as they satisfy a natural reciprocity property. (JEL C78, D82)

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