10,200 research outputs found
Strategyproof matching with regional minimum and maximum quotas
This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare
Integer programming methods for special college admissions problems
We develop Integer Programming (IP) solutions for some special college
admission problems arising from the Hungarian higher education admission
scheme. We focus on four special features, namely the solution concept of
stable score-limits, the presence of lower and common quotas, and paired
applications. We note that each of the latter three special feature makes the
college admissions problem NP-hard to solve. Currently, a heuristic based on
the Gale-Shapley algorithm is being used in the application. The IP methods
that we propose are not only interesting theoretically, but may also serve as
an alternative solution concept for this practical application, and also for
other ones
Strategyproof and fair matching mechanism for ratio constraints
We introduce a new type of distributional constraints called ratio constraints, which explicitly specify the required balance among schools in two-sided matching. Since ratio constraints do not belong to the known well-behaved class of constraints called M-convex set, developing a fair and strategyproof mechanism that can handle them is challenging. We develop a novel mechanism called quota reduction deferred acceptance (QRDA), which repeatedly applies the standard DA by sequentially reducing artificially introduced maximum quotas. As well as being fair and strategyproof, QRDA always yields a weakly better matching for students compared to a baseline mechanism called artificial cap deferred acceptance (ACDA), which uses predetermined artificial maximum quotas. Finally, we experimentally show that, in terms of student welfare and nonwastefulness, QRDA outperforms ACDA and another fair and strategyproof mechanism called Extended Seat Deferred Acceptance (ESDA), in which ratio constraints are transformed into minimum and maximum quotas
Multi-Stage Generalized Deferred Acceptance Mechanism: Strategyproof Mechanism for Handling General Hereditary Constraints
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-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-convex set.Comment: 23 page
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