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International Journal of Game Theory

, Volume 36, Issue 3–4, pp 621–640 | Cite as

The stability of the equilibrium outcomes in the admission games induced by stable matching rules

  • Marilda Sotomayor
Original Paper

Abstract

A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students’ strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised.

Keywords

Stable matching Nash equilibrium Mechanism Stablematching rule Random stable matching rule 

JEL Classification

C78 D78 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Departamento de EconomiaUniversidade de São PauloSão PauloBrazil

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