Matching with Couples: Stability and Incentives in Large Markets

Kojima, Fuhito; Pathak, Parag A.; Roth, Alvin E.

doi:10.3386/w16028

Cited by 31 publications

(39 citation statements)

References 26 publications

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“…This applies even for the simple case where each hospital has one place only, so when the problem is actually a cfg. However, if the ratio of the couples is relatively small in a large market then a stable matching exists with high probability and sophisticated heuristics may be able to find such solutions (see e.g., [22] and [9]). A new heuristic for this problem can be based on the Scarf algorithm for the stable allocation problem (with contributions), where an edge in the hypergraph represents an application from a couple to a pair of hospitals.…”

Section: Solving the Hospitals Residents Problem With Couplesmentioning

confidence: 99%

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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Abstract. In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf's Lemma. Then we describe the interpretation of these results for matching games. Finally we consider an even more general setting where players' contributions in a joint activity may be different. We show that a stable allocation can be found by the Scarf algorithm in this case as well, and we demonstrate the usage of this method for the hospitals resident problem with couples. This problem is relevant in many practical applications, such as NRMP (National Resident Matching Program).

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Section: Solving the Hospitals Residents Problem With Couplesmentioning

confidence: 99%

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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“…It is also known that a stable matching may not exist (Theorem 10 of Roth [52]), and several positive results from the original matching problem do not carry over (Aldershof and Carducci [2]). Several attempts have been made to obtain positive results, such as determining a preference domain for existence (Klaus and Klijn [33]) and considering a large market (Kojima et al [36]). We refer the reader to Biró and Klijn [9] for a comprehensive survey on this topic.…”

Section: Introductionmentioning

confidence: 99%

Two-Sided Matching With Externalities: A Survey

Bando

Kawasaki

Muto

2016

JORSJ

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The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.

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“…For a comprehensive background, and history of these markets see Kojima et al (2010); Roth (2009). Klaus and Klijn (2005) 1 initiated the study of characterizing markets with couples that have a stable matching.…”

Section: Introductionmentioning

confidence: 99%

Matching with Couples Revisited

2010

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It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability.In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truthtelling is an approximated equilibrium in the game induced by the new matching algorithm.Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.

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Matching with Couples: Stability and Incentives in Large Markets

Cited by 31 publications

References 26 publications

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Two-Sided Matching With Externalities: A Survey

Matching with Couples Revisited

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