Group incentive compatibility for matching with contracts

Hatfield, John William; Kojima, Fuhito

doi:10.1016/j.geb.2009.01.007

Cited by 65 publications

(55 citation statements)

References 23 publications

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“…Hatfield and Milgrom (2005) then extended this result to matching problems (with contracts) for which college preferences are substitutable and satisfy the law of aggregate demand. For the same setting, Hatfield and Kojima (2009) showed that these assumptions actually guarantee group strategyproofness.…”

Section: The College Proposing Deferred Acceptance Algorithmmentioning

confidence: 97%

An analysis of the German university admissions system

Westkamp

2012

Econ Theory

116

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Bonn Graduate School of Economics (BGSE)is gratefully acknowledged.Deutsche Post World Net is a sponsor of the BGSE.An analysis of the German university admissions system * Alexander WestkampChair of Economic Theory II, Economics Department, University of Bonn; e-mail: awest@uni-bonn.de. AbstractThis paper analyzes the sequential admissions procedure for medical subjects at public universities in Germany. Complete information equilibrium outcomes are shown to be characterized by a stability condition that is adapted to the institutional constraints of the German system.I introduce matching problems with complex constraints and the notion of procedural stability. Two simple assumptions guarantee existence of a student optimal procedurally stable matching mechanism that is strategyproof for students. In the context of the German admissions problem, this mechanism weakly Pareto dominates all equilibrium outcomes of the currently employed procedure. Applications to school choice with affirmative action are also discussed.

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Section: The College Proposing Deferred Acceptance Algorithmmentioning

confidence: 97%

An analysis of the German university admissions system

Westkamp

2012

Econ Theory

116

View full text Add to dashboard Cite

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“…Our setup can be trivially embedded in the many-to-one matching model with contracts of Hatfield and Kojima (2009), so the conclusion follows.…”

Section: Proof Of Theoremmentioning

confidence: 70%

“…24 School segregation can be purely racial or, as in Echenique, Fryer and Kaufman (2006), school segregation is measured according to the spectral segregation index of Echenique and Fryer (2006) which uses the intensity of social interactions among the members of a group (see also Cutler and Glaeser (1997)). 25 One benefit of hard bounds is that, it is straightforward to check whether they are implemented or not.…”

Section: Resultsmentioning

confidence: 99%

“…The proof is an application of either Martínez et al (2004) or Hatfield and Kojima (2009). Here, we provide the argument following the latter.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Here, we provide the argument following the latter. Hatfield and Kojima (2009) show, in a many-to-one matching model with contracts, that if the choice functions of schools satisfy substitutability and the law of aggregate demand, then the student proposing deferred acceptance algorithm is group incentive compatible. School c's preferences satisfy law of aggregate demand if for any S ⊆ S ⊆ S, we have |Ch c (S )| ≤ |Ch c (S )|.…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 2 more Smart Citations

School choice with controlled choice constraints: Hard bounds versus soft bounds

Ehlers

Hafalır

Yenmez

et al. 2014

Journal of Economic Theory

191

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Controlled choice over public schools attempts giving options to parents while maintaining diversity, often enforced by setting feasibility constraints with hard upper and lower bounds for each student type. We demonstrate that there might not exist assignments that satisfy standard fairness and non-wastefulness properties; whereas constrained non-wasteful assignments which are fair for same type students always exist.We introduce a "controlled" version of the deferred acceptance algorithm with an improvement stage (CDAAI) that finds a Pareto optimal assignment among such assignments. To achieve fair (across all types) and non-wasteful assignments, we propose the control constraints to be interpreted as soft bounds-flexible limits that regulate school priorities. In this setting, a modified version of the deferred acceptance algorithm (DAASB) finds an assignment that is Pareto optimal among fair assignments while eliciting true preferences. CDAAI and DAASB provide two alternative practical solutions depending on the interpretation of the control constraints.JEL C78, D61, D78, I20. * An earlier version (Ehlers, 2010) of this paper emerged from a joint project of the first author with Atila Abdulkadiroglu. We are grateful for his extensive comments and contribution to that paper. Ehlers acknowledges financial support from the SSHRC (Canada).

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Two-sided strategy-proofness in many-to-many matching markets

Romero‐Medina

Triossi

2020

Int J Game Theory

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We study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets.

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Group incentive compatibility for matching with contracts

Cited by 65 publications

References 23 publications

An analysis of the German university admissions system

An analysis of the German university admissions system

School choice with controlled choice constraints: Hard bounds versus soft bounds

Two-sided strategy-proofness in many-to-many matching markets

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