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The theory of two-sided matching has been extensively developed and appliedto many real-life application domains. As the theory has been applied toincreasingly diverse types of environments, researchers and practitioners haveencountered various forms of distributional constraints. Arguably, the mostgeneral class of distributional constraints would be hereditary constraints; ifa matching is feasible, then any matching that assigns weakly fewer students ateach college is also feasible. However, under general hereditary constraints,it is shown that no strategyproof mechanism exists that simultaneouslysatisfies fairness and weak nonwastefulness, which is an efficiency (students'welfare) requirement weaker than nonwastefulness. We propose a newstrategyproof mechanism that works for hereditary constraints called theMulti-Stage Generalized Deferred Acceptance mechanism (MS-GDA). It uses theGeneralized Deferred Acceptance mechanism (GDA) as a subroutine, which workswhen distributional constraints belong to a well-behaved class calledhereditary M$^\natural$-convex set. We show that GDA satisfies severaldesirable properties, most of which are also preserved in MS-GDA. Weexperimentally show that MS-GDA strikes a good balance between fairness andefficiency (students' welfare) compared to existing strategyproof mechanismswhen distributional constraints are close to an M$^\natural$-convex set.

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