151 research outputs found
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
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
Mix and match: a strategyproof mechanism for multi-hospital kidney exchange
As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal
Truthful Assignment without Money
We study the design of truthful mechanisms that do not use payments for the
generalized assignment problem (GAP) and its variants. An instance of the GAP
consists of a bipartite graph with jobs on one side and machines on the other.
Machines have capacities and edges have values and sizes; the goal is to
construct a welfare maximizing feasible assignment. In our model of private
valuations, motivated by impossibility results, the value and sizes on all
job-machine pairs are public information; however, whether an edge exists or
not in the bipartite graph is a job's private information.
We study several variants of the GAP starting with matching. For the
unweighted version, we give an optimal strategyproof mechanism; for maximum
weight bipartite matching, however, we show give a 2-approximate strategyproof
mechanism and show by a matching lowerbound that this is optimal. Next we study
knapsack-like problems, which are APX-hard. For these problems, we develop a
general LP-based technique that extends the ideas of Lavi and Swamy to reduce
designing a truthful mechanism without money to designing such a mechanism for
the fractional version of the problem, at a loss of a factor equal to the
integrality gap in the approximation ratio. We use this technique to obtain
strategyproof mechanisms with constant approximation ratios for these problems.
We then design an O(log n)-approximate strategyproof mechanism for the GAP by
reducing, with logarithmic loss in the approximation, to our solution for the
value-invariant GAP. Our technique may be of independent interest for designing
truthful mechanisms without money for other LP-based problems.Comment: Extended abstract appears in the 11th ACM Conference on Electronic
Commerce (EC), 201
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
Strategyproof Mechanisms For Group-Fair Facility Location Problems
We study the facility location problems where agents are located on a real
line and divided into groups based on criteria such as ethnicity or age. Our
aim is to design mechanisms to locate a facility to approximately minimize the
costs of groups of agents to the facility fairly while eliciting the agents'
locations truthfully. We first explore various well-motivated group fairness
cost objectives for the problems and show that many natural objectives have an
unbounded approximation ratio. We then consider minimizing the maximum total
group cost and minimizing the average group cost objectives. For these
objectives, we show that existing classical mechanisms (e.g., median) and new
group-based mechanisms provide bounded approximation ratios, where the
group-based mechanisms can achieve better ratios. We also provide lower bounds
for both objectives. To measure fairness between groups and within each group,
we study a new notion of intergroup and intragroup fairness (IIF) . We consider
two IIF objectives and provide mechanisms with tight approximation ratios
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