Top

Social Choice and Welfare

Published in:

17-01-2017 | Original Paper

Strategic schools under the Boston mechanism revisited

Authors: Inácio Bó, C.-Philipp Heller

Published in: Social Choice and Welfare | Issue 3/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Ergin and Sönmez (J Public Econ 90(1):215–237, 2006) showed that for schools it is a dominant strategy to report their preferences truthfully under the Boston mechanism, and that the Nash equilibrium outcomes in undominated strategies of the induced game are stable. We show that these results rely crucially on two assumptions. First, schools need to be restricted to reporting all students as acceptable. Second, students cannot observe the preferences reported by the schools before submitting their own preferences. We show that relaxing either assumption gives schools an incentive to manipulate their reported preferences. We provide a full characterization of undominated strategies for schools and students for the simultaneous move game induced by the Boston mechanism. Nash equilibrium outcomes in undominated strategies of that game may contain unstable matchings. Furthermore, when students observe schools’ preferences before submitting theirs, the subgame perfect Nash equilibria of the sequential game induced by the Boston mechanism may also contain unstable matchings. Finally, we show that schools may have an incentive to manipulate capacities only if students observe the schools’ strategies before submitting their own preferences.

previous article Conformity in voting

next article Social choice correspondences with infinitely many agents: serial dictatorship

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

A truncation strategy leaves the true preference over students unchanged, but might drop some acceptable students.

We abuse notation and consider \(\mu (i)\) as an element of S, instead of a set with an element of S.

There is an alternative concept of sequential mechanisms in the school choice literature due to Dur and Kesten (2014). In their analysis schools are not strategic agents. There are two sets of schools whose seats are filled sequentially. In the first round students are matched to one of the schools in the first set, based solely on their preferences over those schools. In the second round, students who were left unmatched in the first round are matched to the second set of schools. In their case “sequential” thus refers to sequentially making an allocation decision. This allows us to use different matching rules, such as the Boston mechanism, top trading cycles or deferred acceptance for different rounds. In contrast, “sequential” in our paper refers to schools submitting their preferences before the students with a fixed mechanism.

For example, all students could declare all schools unacceptable if only at least one school is truthful but otherwise report preferences truthfully. In that case there is at least one school which would gain by deviating from truth-telling. In our view, such strategies for the students can be considered “unreasonable.”

The idea behind this definition is not that it is a property that is necessarily of independent interest. Rather it is a definition that allows us to precisely discuss how the Boston mechanism may give schools an incentive to misrepresent their preferences if students observe the schools’ reports before submitting theirs.

This rules out manipulating by declaring students unacceptable.

When manipulating capacities, a mechanism cannot assign more students to a school than its stated capacities. In New York schools clearly received more students than was possible in their initially declared capacity quota.

This is the famous Rural Hospitals Theorem of Roth (1986).

For this example it is not necessary to specify the preferences of school \(s_{2}\) beyond its ranking over singleton sets of students.

Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93(3):729–747CrossRef

Abdulkadiroğlu A, Pathak PA, Roth AE, Sönmez T (2005a) The Boston public school match. Am Econ Rev 95(2):368–371CrossRef

Abdulkadiroğlu A, Pathak PA, Roth AE (2005b) The New York city high school match. Am Econ Rev 95(2):364–367CrossRef

Abdulkadiroğlu A, Che Y-K, Yasuda Y (2011) Resolving conflicting preferences in school choice: the “Boston mechanism” reconsidered. Am Econ Rev 101(1):399–410CrossRef

Basteck C, Huesmann K, Nax H (2015) Matching practices for secondary schools—Germany, MiP Country Profile 21

Chen L (2012) Matching practices for elementary schools—Ireland, MiP Country Profile 10

De Haan M, Gautier PA, Oosterbeek H, Van der Klaauw B (2015) The performance of school assignment mechanisms in practice, CEPR Discussion Paper No DP10656

Dur U (2015) The modified Boston mechanism. Working Paper, April 2015

Dur U, Kesten O (2014) Sequential versus simultaneous assignment systems and two applications. Working Paper

Ehlers L (2008) Truncation strategies in matching markets. Math Oper Res 33(2):327–335CrossRef

Ehlers L (2010) Manipulation via capacities revisited. Games Econ Behav 69(2):302–311CrossRef

Ergin H, Sönmez T (2006) Games of school choice under the Boston mechanism. J Public Econ 90(1):215–237CrossRef

Featherstone CR, Mayefsky E (2015) Why do some clearinghouses yield stable outcomes? Experimental evidence on out-of-equilibrium truth-telling. Working Paper

Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15CrossRef

Kojima F (2008) Games of school choice under the Boston mechanism with general priority structures. Soc Choice Welf 31(3):357–365CrossRef

Kojima F, Ünver MU (2014) The “Boston” school-choice mechanism: an axiomatic approach. Econ Theory 55(3):515–544CrossRef

Kojima F, Pathak PA (2009) Incentives and stability in large two-sided matching markets. Am Econ Rev 99(3):608–627CrossRef

Konishi H, Ünver MU (2006) Games of capacity manipulation in hospital-intern markets. Soc Choice Welf 27(1):3–24CrossRef

Mennle T, Seuken S (2014) The Naïve versus the adaptive Boston mechanism. Working Paper

Miralles A (2009) School choice: the case for the Boston mechanism. In: Auctions, market mechanisms and their applications. Springer, Berlin, pp 58–60

Pais J, Pintér Á (2008) School choice and information: an experimental study on matching mechanisms. Games Econ Behav 64(1):303–328CrossRef

Pathak PA, Sönmez T (2008) Leveling the playing field: sincere and sophisticated players in the Boston mechanism. Am Econ Rev 98(4):1636–1652CrossRef

Pathak PA, Sönmez T (2013) School admissions reform in Chicago and England: comparing mechanisms by their vulnerability to manipulation. Am Econ Rev 103(1):80–106CrossRef

Romero-Medina A, Triossi M (2013) Games with capacity manipulation: incentives and Nash equilibria. Soc Choice Welf 41(3):701–720CrossRef

Roth AE (1986) On the allocation of residents to rural hospitals: a general property of two-sided matching markets. Econometrica 54(2):425–427CrossRef

Roth AE (1991) A natural experiment in the organization of entry-level labor markets: regional markets for new physicians and surgeons in the United Kingdom. Am Econ Rev 81(3):415–440

Roth AE, Postlewaite A (1977) Weak versus strong domination in a market with indivisible goods. J Math Econ 4(2):131–137CrossRef

Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis, vol 18. Cambridge University Press, CambridgeCrossRef

Title: Strategic schools under the Boston mechanism revisited
Authors: Inácio Bó
C.-Philipp Heller
Publication date: 17-01-2017
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 3/2017
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-1024-6

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2017

Characterising competitive equilibrium in terms of opportunity

Properties of multiwinner voting rules

Conformity in voting

First-mover advantage in round-robin tournaments

Strategy-proofness of the randomized Condorcet voting system

Social choice correspondences with infinitely many agents: serial dictatorship