# Strategic schools under the Boston mechanism revisited

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## 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.

### References

- Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93(3):729–747CrossRefGoogle Scholar
- Abdulkadiroğlu A, Pathak PA, Roth AE, Sönmez T (2005a) The Boston public school match. Am Econ Rev 95(2):368–371CrossRefGoogle Scholar
- Abdulkadiroğlu A, Pathak PA, Roth AE (2005b) The New York city high school match. Am Econ Rev 95(2):364–367CrossRefGoogle Scholar
- Abdulkadiroğlu A, Che Y-K, Yasuda Y (2011) Resolving conflicting preferences in school choice: the “Boston mechanism” reconsidered. Am Econ Rev 101(1):399–410CrossRefGoogle Scholar
- Basteck C, Huesmann K, Nax H (2015) Matching practices for secondary schools—Germany, MiP Country Profile 21Google Scholar
- Chen L (2012) Matching practices for elementary schools—Ireland, MiP Country Profile 10Google Scholar
- De Haan M, Gautier PA, Oosterbeek H, Van der Klaauw B (2015) The performance of school assignment mechanisms in practice, CEPR Discussion Paper No DP10656Google Scholar
- Dur U (2015) The modified Boston mechanism. Working Paper, April 2015Google Scholar
- Dur U, Kesten O (2014) Sequential versus simultaneous assignment systems and two applications. Working PaperGoogle Scholar
- Ehlers L (2008) Truncation strategies in matching markets. Math Oper Res 33(2):327–335CrossRefGoogle Scholar
- Ehlers L (2010) Manipulation via capacities revisited. Games Econ Behav 69(2):302–311CrossRefGoogle Scholar
- Ergin H, Sönmez T (2006) Games of school choice under the Boston mechanism. J Public Econ 90(1):215–237CrossRefGoogle Scholar
- Featherstone CR, Mayefsky E (2015) Why do some clearinghouses yield stable outcomes? Experimental evidence on out-of-equilibrium truth-telling. Working PaperGoogle Scholar
- Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15CrossRefGoogle Scholar
- Kojima F (2008) Games of school choice under the Boston mechanism with general priority structures. Soc Choice Welf 31(3):357–365CrossRefGoogle Scholar
- Kojima F, Ünver MU (2014) The “Boston” school-choice mechanism: an axiomatic approach. Econ Theory 55(3):515–544CrossRefGoogle Scholar
- Kojima F, Pathak PA (2009) Incentives and stability in large two-sided matching markets. Am Econ Rev 99(3):608–627CrossRefGoogle Scholar
- Konishi H, Ünver MU (2006) Games of capacity manipulation in hospital-intern markets. Soc Choice Welf 27(1):3–24CrossRefGoogle Scholar
- Mennle T, Seuken S (2014) The Naïve versus the adaptive Boston mechanism. Working PaperGoogle Scholar
- Miralles A (2009) School choice: the case for the Boston mechanism. In: Auctions, market mechanisms and their applications. Springer, Berlin, pp 58–60Google Scholar
- Pais J, Pintér Á (2008) School choice and information: an experimental study on matching mechanisms. Games Econ Behav 64(1):303–328CrossRefGoogle Scholar
- Pathak PA, Sönmez T (2008) Leveling the playing field: sincere and sophisticated players in the Boston mechanism. Am Econ Rev 98(4):1636–1652CrossRefGoogle Scholar
- Pathak PA, Sönmez T (2013) School admissions reform in Chicago and England: comparing mechanisms by their vulnerability to manipulation. Am Econ Rev 103(1):80–106CrossRefGoogle Scholar
- Romero-Medina A, Triossi M (2013) Games with capacity manipulation: incentives and Nash equilibria. Soc Choice Welf 41(3):701–720CrossRefGoogle Scholar
- Roth AE (1986) On the allocation of residents to rural hospitals: a general property of two-sided matching markets. Econometrica 54(2):425–427CrossRefGoogle Scholar
- 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):415–440Google Scholar
- Roth AE, Postlewaite A (1977) Weak versus strong domination in a market with indivisible goods. J Math Econ 4(2):131–137CrossRefGoogle Scholar
- Roth AE, Sotomayor MAO (1990) Two-sided matching: a study in game-theoretic modeling and analysis, vol 18. Cambridge University Press, CambridgeCrossRefGoogle Scholar