Matching with Generalized Sequential Choice Rules

TL;DR

This paper introduces a flexible family of choice rules called generalized sequential (GSq) for many-to-one matching problems involving institutions with multiple divisions and constraints, demonstrating the stability and strategy-proofness of the cumulative offer mechanism (COM) under these rules.

Contribution

It defines the GSq family of choice rules, proves COM's uniqueness as a stable and strategy-proof mechanism under GSq, and shows real-world applications in education and employment markets.

Findings

COM is the unique stable, strategy-proof mechanism under GSq.

GSq encompasses many practical choice rules.

Applications include Indian higher education and Chinese high school admissions.

Abstract

This paper studies a many-to-one matching between individuals and institutions where institutions comprise multiple divisions and face cross-divisional constraints. We introduce a parametrized family of choice rules, which we call generalized sequential (GSq), that encompasses many different choice rules encountered in practice and in market design literature. We show that the cumulative offer mechanism (COM) is the unique stable and strategy-proof mechanism in a matching problem where all institutions have a GSq choice rule. We present two real-world applications in which choice rules in the GSq family emerge naturally: affirmative action in India's public higher educational institutions and government jobs, and high school admissions in China.