Multi-Stage Generalized Deferred Acceptance Mechanism: Strategyproof Mechanism for Handling General Hereditary Constraints

TL;DR

This paper introduces the Multi-Stage Generalized Deferred Acceptance mechanism (MS-GDA), a strategyproof approach for matching under hereditary constraints that balances fairness and efficiency.

Contribution

It proposes a novel multi-stage mechanism that extends the Generalized Deferred Acceptance to handle hereditary constraints, ensuring strategyproofness and desirable properties.

Findings

MS-GDA maintains strategyproofness under hereditary constraints.

Experimental results show MS-GDA balances fairness and student welfare effectively.

GDA satisfies key properties, many preserved in MS-GDA.

Abstract

The theory of two-sided matching has been extensively developed and applied to many real-life application domains. As the theory has been applied to increasingly diverse types of environments, researchers and practitioners have encountered various forms of distributional constraints. Arguably, the most general class of distributional constraints would be hereditary constraints; if a matching is feasible, then any matching that assigns weakly fewer students at each college is also feasible. However, under general hereditary constraints, it is shown that no strategyproof mechanism exists that simultaneously satisfies fairness and weak nonwastefulness, which is an efficiency (students' welfare) requirement weaker than nonwastefulness. We propose a new strategyproof mechanism that works for hereditary constraints called the Multi-Stage Generalized Deferred Acceptance mechanism (MS-GDA). It uses the Generalized Deferred Acceptance mechanism (GDA) as a subroutine, which works when distributional constraints belong to a well-behaved class called hereditary M$^\natural$-convex set. We show that GDA satisfies several desirable properties, most of which are also preserved in MS-GDA. We experimentally show that MS-GDA strikes a good balance between fairness and efficiency (students' welfare) compared to existing strategyproof mechanisms when distributional constraints are close to an M$^\natural$-convex set.