TITLE:
Passively-Strictly Strong Nash Equilibrium in a Preference Revelation Game under the Student-Optimal Deferred Acceptance Algorithm
AUTHORS:
Chengyue Li, Takehiro Inohara, Masahito Kitamura
KEYWORDS:
Student-Optimal Deferred Acceptance Algorithm, Preference Revelation Game, Passively-Strictly Strong Nash Equilibrium
JOURNAL NAME:
Theoretical Economics Letters,
Vol.7 No.5,
July
31,
2017
ABSTRACT: 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.