On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

Bando, Keisuke

doi:10.1016/j.geb.2014.05.009

Cited by 32 publications

(22 citation statements)

References 21 publications

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“…Hence the existence problem of SSN becomes one of the focuses in the later research. Bando [4] demonstrated the existence of the following two SSNs.…”

Section: College Admission Marketmentioning

confidence: 97%

“…Roth [10] and Bando [4] demonstrated that if a coalition S has a successful deviation (either in a strong sense or in a weak sense), then it equals to using a simplified strategy that each student in S reports the deviating outcome as her first choice. Therefore, we also consider this kind of simple deviation in this research.…”

Section: Existencementioning

confidence: 99%

“…Dubins and Freedman [3] demonstrated that the truth-telling strategy profile is a SN. However, Bando [4], Dubins and Freedman [3] and Sotomayor [5] all showed that it does not satisfy a stronger equilibrium concept, in the sense that none of the student groups can make all its members weakly better off and at least one member strictly better off by changing their joint strategies.…”

Section: Introductionmentioning

confidence: 99%

“…Bando [4] formally named this equilibrium concept as strictly strong Nash equilibrium (SSN). He then demonstrated the existence of two SSNs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Passively-Strictly Strong Nash Equilibrium in a Preference Revelation Game under the Student-Optimal Deferred Acceptance Algorithm

Li¹,

Inohara²,

Kitamura³

2017

TEL

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We revisit a college admission market and a related preference revelation game under the student-optimal deferred acceptance algorithm (SODA). Previous research has demonstrated the existence of a strictly strong Nash equilibrium (SSN) based on either an iterative deferred acceptance algorithm (DA-SSN) or the core of a corresponding house allocation problem (Core-SSN). We propose a new equilibrium concept called passively-strictly strong Nash equilibrium (P-SSN). It rules out a kind of deviation called passively weak deviation which includes students who were threatened to deviate. Then we show two preliminary existence results about P-SSN. (i) If the DA-SSN and the Core-SSN are not equivalent, then neither of them is a P-SSN. (ii) If the matching determined by the DA-SSN satisfies a property called irrelevance of low-tier agents, then the DA-SSN is also a P-SSN.

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“…Hence the existence problem of SSN becomes one of the focuses in the later research. Bando [4] demonstrated the existence of the following two SSNs.…”

Section: College Admission Marketmentioning

confidence: 97%

Section: Existencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Bando [4] formally named this equilibrium concept as strictly strong Nash equilibrium (SSN). He then demonstrated the existence of two SSNs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Passively-Strictly Strong Nash Equilibrium in a Preference Revelation Game under the Student-Optimal Deferred Acceptance Algorithm

Li¹,

Inohara²,

Kitamura³

2017

TEL

View full text Add to dashboard Cite

show abstract

“…Bando [4] shows that the EADAM outcome can be supported by a strictly strong Nash equilibrium of the preference revelation game under DA, and along the way independently proposes another simplification of Kesten's EADAM. Bando's algorithm focuses on the removal of the last-step proposers of the DA algorithm, instead of the lastly rejected interrupters.…”

Section: Introductionmentioning

confidence: 97%