Stability and the immediate acceptance rule when school priorities are weak

Wonki Cho, Battal Doğan

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)991-1014
Number of pages24
JournalInternational Journal of Game Theory
Issue number4
Publication statusPublished - 2017 Nov 1
Externally publishedYes


  • Immediate acceptance
  • School choice
  • Stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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