22,331 research outputs found
Social Welfare in One-Sided Matching Mechanisms
We study the Price of Anarchy of mechanisms for the well-known problem of
one-sided matching, or house allocation, with respect to the social welfare
objective. We consider both ordinal mechanisms, where agents submit preference
lists over the items, and cardinal mechanisms, where agents may submit
numerical values for the items being allocated. We present a general lower
bound of on the Price of Anarchy, which applies to all
mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and
Random Priority, achieve a matching upper bound. We extend our lower bound to
the Price of Stability of a large class of mechanisms that satisfy a common
proportionality property, and show stronger bounds on the Price of Anarchy of
all deterministic mechanisms
Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching
We study the efficiency (in terms of social welfare) of truthful and
symmetric mechanisms in one-sided matching problems with {\em dichotomous
preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are
particularly interested in the well-known {\em Random Serial Dictatorship}
mechanism. For dichotomous preferences, we first show that truthful, symmetric
and optimal mechanisms exist if intractable mechanisms are allowed. We then
provide a connection to online bipartite matching. Using this connection, it is
possible to design truthful, symmetric and tractable mechanisms that extract
0.69 of the maximum social welfare, which works under assumption that agents
are not adversarial. Without this assumption, we show that Random Serial
Dictatorship always returns an assignment in which the expected social welfare
is at least a third of the maximum social welfare. For normalized von
Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always
returns an assignment in which the expected social welfare is at least
\frac{1}{e}\frac{\nu(\opt)^2}{n}, where \nu(\opt) is the maximum social
welfare and is the number of both agents and items. On the hardness side,
we show that no truthful mechanism can achieve a social welfare better than
\frac{\nu(\opt)^2}{n}.Comment: 13 pages, 1 figur
Don’t Roll the Dice, Ask Twice: The Two-Query Distortion of Matching Problems and Beyond
In most social choice settings, the participating agents are typically
required to express their preferences over the different alternatives in the
form of linear orderings. While this simplifies preference elicitation, it
inevitably leads to high distortion when aiming to optimize a cardinal
objective such as the social welfare, since the values of the agents remain
virtually unknown. A recent array of works put forward the agenda of designing
mechanisms that can learn the values of the agents for a small number of
alternatives via queries, and use this extra information to make a
better-informed decision, thus improving distortion. Following this agenda, in
this work we focus on a class of combinatorial problems that includes most
well-known matching problems and several of their generalizations, such as
One-Sided Matching, Two-Sided Matching, General Graph Matching, and
-Constrained Resource Allocation. We design two-query mechanisms that
achieve the best-possible worst-case distortion in terms of social welfare, and
outperform the best-possible expected distortion that can be achieved by
randomized ordinal mechanisms
Social Welfare in One-sided Matching Markets without Money
We study social welfare in one-sided matching markets where the goal is to
efficiently allocate n items to n agents that each have a complete, private
preference list and a unit demand over the items. Our focus is on allocation
mechanisms that do not involve any monetary payments. We consider two natural
measures of social welfare: the ordinal welfare factor which measures the
number of agents that are at least as happy as in some unknown, arbitrary
benchmark allocation, and the linear welfare factor which assumes an agent's
utility linearly decreases down his preference lists, and measures the total
utility to that achieved by an optimal allocation. We analyze two matching
mechanisms which have been extensively studied by economists. The first
mechanism is the random serial dictatorship (RSD) where agents are ordered in
accordance with a randomly chosen permutation, and are successively allocated
their best choice among the unallocated items. The second mechanism is the
probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which
computes a fractional allocation that can be expressed as a convex combination
of integral allocations. The welfare factor of a mechanism is the infimum over
all instances. For RSD, we show that the ordinal welfare factor is
asymptotically 1/2, while the linear welfare factor lies in the interval [.526,
2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the
linear welfare factor is roughly 2/3. To our knowledge, these results are the
first non-trivial performance guarantees for these natural mechanisms
Welfare Maximization and Truthfulness in Mechanism Design with Ordinal Preferences
We study mechanism design problems in the {\em ordinal setting} wherein the
preferences of agents are described by orderings over outcomes, as opposed to
specific numerical values associated with them. This setting is relevant when
agents can compare outcomes, but aren't able to evaluate precise utilities for
them. Such a situation arises in diverse contexts including voting and matching
markets.
Our paper addresses two issues that arise in ordinal mechanism design. To
design social welfare maximizing mechanisms, one needs to be able to
quantitatively measure the welfare of an outcome which is not clear in the
ordinal setting. Second, since the impossibility results of Gibbard and
Satterthwaite~\cite{Gibbard73,Satterthwaite75} force one to move to randomized
mechanisms, one needs a more nuanced notion of truthfulness.
We propose {\em rank approximation} as a metric for measuring the quality of
an outcome, which allows us to evaluate mechanisms based on worst-case
performance, and {\em lex-truthfulness} as a notion of truthfulness for
randomized ordinal mechanisms. Lex-truthfulness is stronger than notions
studied in the literature, and yet flexible enough to admit a rich class of
mechanisms {\em circumventing classical impossibility results}. We demonstrate
the usefulness of the above notions by devising lex-truthful mechanisms
achieving good rank-approximation factors, both in the general ordinal setting,
as well as structured settings such as {\em (one-sided) matching markets}, and
its generalizations, {\em matroid} and {\em scheduling} markets.Comment: Some typos correcte
Social welfare in one-sided matchings: Random priority and beyond
We study the problem of approximate social welfare maximization (without
money) in one-sided matching problems when agents have unrestricted cardinal
preferences over a finite set of items. Random priority is a very well-known
truthful-in-expectation mechanism for the problem. We prove that the
approximation ratio of random priority is Theta(n^{-1/2}) while no
truthful-in-expectation mechanism can achieve an approximation ratio better
than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we
prove that the approximation ratio of all ordinal (not necessarily
truthful-in-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating
that random priority is asymptotically the best truthful-in-expectation
mechanism and the best ordinal mechanism for the problem.Comment: 13 page
Filling position incentives in matching markets
One of the main problems in the hospital-doctor matching is the maldistribution of doctor assignments across hospitals. Namely, many hospitals in rural areas are matched with far fewer doctors than what they need. The so called "Rural Hospital Theorem" (Roth (1984)) reveals that it is unavoidable under stable assignments. On the other hand, the counterpart of the problem in the school choice context|low enrollments at schools| has important consequences for schools as well. In the current study, we approach the problem from a
different point of view and investigate whether hospitals can increase their filled positions by misreporting their preferences under well-known Boston, Top Trading Cycles, and stable rules. It turns out that while it is impossible under Boston and stable mechanisms, Top Trading Cycles rule is manipulable in that sense
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