## Abstract

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann-Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.

Original language | English |
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Pages (from-to) | 269-287 |

Number of pages | 19 |

Journal | Games and Economic Behavior |

Volume | 87 |

DOIs | |

Publication status | Published - 2014 Sept |

Externally published | Yes |

## Keywords

- Efficiency-adjusted deferred acceptance algorithm
- Strictly strong Nash equilibrium
- Student-optimal deferred acceptance algorithm
- Student-optimal vNM stable matching

## ASJC Scopus subject areas

- Finance
- Economics and Econometrics