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

We revisit a college admission market and a relatedpreference revelation game under the student-optimal deferred acceptancealgorithm (SODA). Previous research has demonstrated the existence of astrictly strong Nash equilibrium (SSN) based on either an iterative deferredacceptance algorithm (DA-SSN) or the core of a corresponding house allocationproblem (Core-SSN). We propose a new equilibrium concept calledpassively-strictly strong Nash equilibrium (P-SSN). It rules out a kind ofdeviation called passively weak deviation which includes students who werethreatened 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 isa P-SSN. (ii) If the matching determined by the DA-SSN satisfies a property called irrelevance oflow-tier agents, then the DA-SSN is also a P-SSN.