9,842 research outputs found
Designing Matching Mechanisms under General Distributional Constraints
In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and ``more fair'' than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and ``less wasteful'' than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains
Designing Matching Mechanisms under General Distributional Constraints
In this paper, we consider two-sided, many-to-one matching problems where agents in one side of the market (schools) impose some distributional constraints (e.g., a maximum quota for a set of schools), and develop a strategyproof mechanism that can handle a very general class of distributional constraints. We assume distributional constraints are imposed on a vector, where each element is the number of contracts accepted for each school. The only requirement we impose on distributional constraints is that the family of vectors that satisfy distributional constraints must be hereditary, which means if a vector satisfies the constraints, any vector that is smaller than it also satisfies them. When distributional constraints are imposed, a stable matching may not exist. We develop a strategyproof mechanism called Adaptive Deferred Acceptance mechanism (ADA), which is nonwasteful and ``more fair'' than a simple nonwasteful mechanism called the Serial Dictatorship mechanism (SD) and ``less wasteful'' than another simple fair mechanism called the Artificial Cap Deferred Acceptance mechanism (ACDA). We show that we can apply this mechanism even if the distributional constraints do not satisfy the hereditary condition by applying a simple trick, assuming we can find a vector that satisfy the distributional constraints efficiently. Furthermore, we demonstrate the applicability of our model in actual application domains
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
Dynamic Reserves in Matching Markets
We study a school choice problem under affirmative action policies where
authorities reserve a certain fraction of the slots at each school for specific
student groups, and where students have preferences not only over the schools
they are matched to but also the type of slots they receive. Such reservation
policies might cause waste in instances of low demand from some student groups.
To propose a solution to this issue, we construct a family of choice functions,
dynamic reserves choice functions, for schools that respect within-group
fairness and allow the transfer of otherwise vacant slots from low-demand
groups to high-demand groups. We propose the cumulative offer mechanism (COM)
as an allocation rule where each school uses a dynamic reserves choice function
and show that it is stable with respect to schools' choice functions, is
strategy-proof, and respects improvements. Furthermore, we show that
transferring more of the otherwise vacant slots leads to strategy-proof Pareto
improvement under the COM
How should public infrastructure be financed?
Infrastructure (Economics) ; Finance ; Public policy
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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