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)

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 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 Weighted Matching Markets with Budget Constraints

2019 ◽  
Vol 65 ◽  
pp. 393-421 ◽  
Author(s):  
Anisse Ismaili ◽  
Naoto Hamada ◽  
Yuzhe Zhang ◽  
Takamasa Suzuki ◽  
Makoto Yokoo
Keyword(s):  
Polynomial Time ◽  
Real World ◽  
Stable Matching ◽  
The Other ◽  
Matching Markets ◽  
Pairwise Stability ◽  
Negative Results ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
Coalitional Stability

We investigate markets with a set of students on one side and a set of colleges on the other. A student and college can be linked by a weighted contract that defines the student's wage, while a college's budget for hiring students is limited. Stability is a crucial requirement for matching mechanisms to be applied in the real world. A standard stability requirement is coalitional stability, i.e., no pair of a college and group of students has any incentive to deviate. We find that a coalitionally stable matching is not guaranteed to exist, verifying the coalitional stability for a given matching is coNP-complete, and the problem of finding whether a coalitionally stable matching exists in a given market, is SigmaP2-complete: NPNP-complete. Other negative results also hold when blocking coalitions contain at most two students and one college. Given these computational hardness results, we pursue a weaker stability requirement called pairwise stability, where no pair of a college and single student has an incentive to deviate. Unfortunately, a pairwise stable matching is not guaranteed to exist either. Thus, we consider a restricted market called a typed weighted market, in which students are partitioned into types that induce their possible wages. We then design a strategy-proof and Pareto efficient mechanism that works in polynomial-time for computing a pairwise stable matching in typed weighted markets.

scholarly journals Finding Robust Solutions to Stable Marriage

2017 ◽  
Author(s):  
Begum Genc ◽  
Mohamed Siala ◽  
Barry O'Sullivan ◽  
Gilles Simonin
Keyword(s):  
Local Search ◽  
Programming Model ◽  
Empirical Evaluation ◽  
Stable Matching ◽  
The Other ◽  
Stable Marriage ◽  
Matching Problems ◽  
Robust Solutions ◽  
Constraint Programming Model ◽  
Search Approach

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.

scholarly journals The Maximum-Weight Stable Matching Problem: Duality and Efficiency

2012 ◽  
Vol 26 (3) ◽  
pp. 1346-1360 ◽  
Author(s):  
Xujin Chen ◽  
Guoli Ding ◽  
Xiaodong Hu ◽  
Wenan Zang
Keyword(s):  
Stable Matching ◽  
Maximum Weight ◽  
Matching Problem

scholarly journals Stable Matchings with Diversity Constraints: Affirmative Action is beyond NP

2020 ◽  
Author(s):  
Jiehua Chen ◽  
Robert Ganian ◽  
Thekla Hamm
Keyword(s):  
Affirmative Action ◽  
Stable Matching ◽  
Comprehensive Analysis ◽  
Complexity Class ◽  
Np Hard ◽  
Matching Problem ◽  
Stable Matchings ◽  
Student College ◽  
Total Capacity ◽  
New Algorithms

We investigate the following many-to-one stable matching problem with diversity constraints (SMTI-DIVERSE): Given a set of students and a set of colleges which have preferences over each other, where the students have overlapping types, and the colleges each have a total capacity as well as quotas for individual types (the diversity constraints), is there a matching satisfying all diversity constraints such that no unmatched student-college pair has an incentive to deviate? SMTI-DIVERSE is known to be NP-hard. However, as opposed to the NP-membership claims in the literature [Aziz et al., AAMAS 2019; Huang,SODA 2010], we prove that it is beyond NP: it is complete for the complexity class Σ^P_2. In addition, we provide a comprehensive analysis of the problem’s complexity from the viewpoint of natural restrictions to inputs and obtain new algorithms for the problem.

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