International Journal of Game Theory

, Volume 46, Issue 4, pp 991–1014 | Cite as

Stability and the immediate acceptance rule when school priorities are weak

  • Wonki Jo Cho
  • Battal Doğan
Original Paper


In a model of school choice, we allow school priorities to be weak and study the preference revelation game induced by the immediate acceptance (IA) rule (also known as the Boston rule), or the IA game. When school priorities can be weak and matches probabilistic, three stability notions—ex post stability, ex ante stability, and strong ex ante stability—and two ordinal equilibrium notions—sd equilibrium and strong sd equilibrium—become available (“sd” stands for stochastic dominance). We show that for no combination of stability and equilibrium notions does the set of stable matches coincide with the set of equilibrium matches of the IA game. This stands in contrast with the existing result that the two sets are equal when priorities are strict. We also show that in the presence of weak priorities, the transition from the IA rule to the deferred acceptance rule may, in fact, harm some students.


School choice Stability Immediate acceptance 

JEL Classification

C78 D71 D78 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of EconomicsSogang UniversitySeoulRepublic of Korea
  2. 2.Faculty of Business and EconomicsUniversity of LausanneLausanneSwitzerland

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