Essentially stable matchings

Troyan, Peter; Delacrétaz, David; Kloosterman, Andrew

doi:10.1016/j.geb.2020.01.009

Cited by 39 publications

(15 citation statements)

References 38 publications

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“…In settings without transfers, in addition to Gibbard (1973Gibbard ( , 1977 and Satterthwaite (1975) and the allocation papers mentioned above, the literature on mechanisms satisfying these key objectives includes Pápai (2000), Ehlers (2002) and Pycia and Unver (2020; who characterized efficient and group strategy-proof mechanisms in settings with single-unit demand, and Pápai (2001) and Hatfield (2009) who provided such characterizations for settings with multi-unit demand. 14 Liu and Pycia (2011), Pycia (2011), Morrill (2014, Hakimov and Kesten (2014), Ehlers and Morrill (2017), and Troyan et al (2020) characterize mechanisms that satisfy incentive, efficiency, and fairness objectives.…”

Section: Introductionmentioning

confidence: 99%

A Theory of Simplicity in Games and Mechanism Design

Pycia

Troyan

2021

SSRN Journal

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We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our gradated approach to simplicity to provide characterizations of simple mechanisms. While more demanding simplicity standards may reduce the flexibility of the designer in some cases, this is not always true, and many well-known mechanisms are simple, including ascending auctions, posted prices, and serial dictatorship-style mechanisms. In particular, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.

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Section: Introductionmentioning

confidence: 99%

A Theory of Simplicity in Games and Mechanism Design

Pycia

Troyan

2021

SSRN Journal

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“…6 See Section 4 for a definition of an improvement cycle 7 Dogan and Yenmez (2020), Dur et al (2019), Ehlers and Morrill (2020), Kwon and Shorrer (2019), Tang and Zhang (2020), and Troyan et al (2020) provide different other justifications for EADA. school choice mechanisms are compared in terms of their manipulability by comparing the sets of problems, in the set inclusion sense, at which they are manipulable.…”

Section: Introductionmentioning

confidence: 99%

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

Doğan

Ehlers

2020

SSRN Journal

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It is known that there are school choice problems without an efficient and stable assignment. We consider comparing assignments in terms of their stability by comparing their sets of blocking (student-school) pairs or comparing their sets of blocking students who are involved in at least one blocking pair. Although there always exists a Pareto improvement over the student-optimal stable (DA) assignment which is minimally unstable among efficient assignments when the stability comparison is based on comparing the sets of blocking pairs in the set-inclusion sense, we show that this is not necessarily true when the stability comparison is based on comparing the sets of blocking pairs in the cardinal sense, or when it is based on comparing sets of blocking students (in the set-inclusion or cardinal sense). Given the latter impossibilities, we characterize the priority profiles where there exists a Pareto improvement over the DA mechanism which is cardinally minimally stable among efficient assignments when counting blocking pairs or counting blocking students. The resulting domain restrictions suggest to take with caution school choice analysis which relies on a particular stability comparison method.

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“…They show that the SOSM is the only stable‐dominating and strategy‐proof rule. Troyan et al () and Morrill () focus on the alternative ways to improve efficiency by relaxing the fairness constraint. In particular, under the Morrill () definition of fairness , a student i 's priority at school s needs to be respected only if there exists a textitlegitimate matching in which i is assigned to s .…”

Section: Introductionmentioning

confidence: 99%

“…He shows that there is a unique legitimate set of matchings and a unique Pareto efficient and legitimate matching which corresponds to EADAM's outcome when all students consent. According to Troyan et al (), a matching is essentially stable if any objection of student i to her priority violation at school s initiates a rejection chain that results in her rejection from s . They show that the EADAM produces an essentially stable matching.…”

Section: Introductionmentioning

confidence: 99%

School choice under partial fairness

Dur¹,

Gitmez

Yılmaz³

2019

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We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the student exchange under partial fairness (SEPF). Each member of this class gives a partially stable matching that is not Pareto dominated by another partially stable matching (i.e., constrained efficient in the class of partially stable matchings). Moreover, any constrained efficient matching that Pareto improves upon a partially stable matching can be obtained via an algorithm within the SEPF class. We characterize the unique algorithm in the SEPF class that satisfies a desirable incentive property. The extension of the model to an environment with weak priorities enables us to provide a characterization result that proves the counterpart of the main result in Erdil and Ergin (2008).

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Essentially stable matchings

Cited by 39 publications

References 38 publications

A Theory of Simplicity in Games and Mechanism Design

A Theory of Simplicity in Games and Mechanism Design

Blocking Pairs Versus Blocking Students: Stability Comparisons in School Choice

School choice under partial fairness

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