1,589 research outputs found
Budget Feasible Mechanisms
We study a novel class of mechanism design problems in which the outcomes are
constrained by the payments. This basic class of mechanism design problems
captures many common economic situations, and yet it has not been studied, to
our knowledge, in the past. We focus on the case of procurement auctions in
which sellers have private costs, and the auctioneer aims to maximize a utility
function on subsets of items, under the constraint that the sum of the payments
provided by the mechanism does not exceed a given budget. Standard mechanism
design ideas such as the VCG mechanism and its variants are not applicable
here. We show that, for general functions, the budget constraint can render
mechanisms arbitrarily bad in terms of the utility of the buyer. However, our
main result shows that for the important class of submodular functions, a
bounded approximation ratio is achievable. Better approximation results are
obtained for subclasses of the submodular functions. We explore the space of
budget feasible mechanisms in other domains and give a characterization under
more restricted conditions
Truthful Mechanisms for Matching and Clustering in an Ordinal World
We study truthful mechanisms for matching and related problems in a partial
information setting, where the agents' true utilities are hidden, and the
algorithm only has access to ordinal preference information. Our model is
motivated by the fact that in many settings, agents cannot express the
numerical values of their utility for different outcomes, but are still able to
rank the outcomes in their order of preference. Specifically, we study problems
where the ground truth exists in the form of a weighted graph of agent
utilities, but the algorithm can only elicit the agents' private information in
the form of a preference ordering for each agent induced by the underlying
weights. Against this backdrop, we design truthful algorithms to approximate
the true optimum solution with respect to the hidden weights. Our techniques
yield universally truthful algorithms for a number of graph problems: a
1.76-approximation algorithm for Max-Weight Matching, 2-approximation algorithm
for Max k-matching, a 6-approximation algorithm for Densest k-subgraph, and a
2-approximation algorithm for Max Traveling Salesman as long as the hidden
weights constitute a metric. We also provide improved approximation algorithms
for such problems when the agents are not able to lie about their preferences.
Our results are the first non-trivial truthful approximation algorithms for
these problems, and indicate that in many situations, we can design robust
algorithms even when the agents may lie and only provide ordinal information
instead of precise utilities.Comment: To appear in the Proceedings of WINE 201
Bribeproof mechanisms for two-values domains
Schummer (Journal of Economic Theory 2000) introduced the concept of
bribeproof mechanism which, in a context where monetary transfer between agents
is possible, requires that manipulations through bribes are ruled out.
Unfortunately, in many domains, the only bribeproof mechanisms are the trivial
ones which return a fixed outcome.
This work presents one of the few constructions of non-trivial bribeproof
mechanisms for these quasi-linear environments. Though the suggested
construction applies to rather restricted domains, the results obtained are
tight: For several natural problems, the method yields the only possible
bribeproof mechanism and no such mechanism is possible on more general domains.Comment: Extended abstract accepted to SAGT 2016. This ArXiv version corrects
typos in the proofs of Theorem 7 and Claims 28-29 of prior ArXiv versio
Budget Feasible Mechanisms for Experimental Design
In the classical experimental design setting, an experimenter E has access to
a population of potential experiment subjects , each
associated with a vector of features . Conducting an experiment
with subject reveals an unknown value to E. E typically assumes
some hypothetical relationship between 's and 's, e.g., , and estimates from experiments, e.g., through linear
regression. As a proxy for various practical constraints, E may select only a
subset of subjects on which to conduct the experiment.
We initiate the study of budgeted mechanisms for experimental design. In this
setting, E has a budget . Each subject declares an associated cost to be part of the experiment, and must be paid at least her cost. In
particular, the Experimental Design Problem (EDP) is to find a set of
subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in
S}x_i\T{x_i}) under the constraint ; our objective
function corresponds to the information gain in parameter that is
learned through linear regression methods, and is related to the so-called
-optimality criterion. Further, the subjects are strategic and may lie about
their costs.
We present a deterministic, polynomial time, budget feasible mechanism
scheme, that is approximately truthful and yields a constant factor
approximation to EDP. In particular, for any small and , we can construct a (12.98, )-approximate mechanism that is
-truthful and runs in polynomial time in both and
. We also establish that no truthful,
budget-feasible algorithms is possible within a factor 2 approximation, and
show how to generalize our approach to a wide class of learning problems,
beyond linear regression
On Simultaneous Two-player Combinatorial Auctions
We consider the following communication problem: Alice and Bob each have some
valuation functions and over subsets of items,
and their goal is to partition the items into in a way that
maximizes the welfare, . We study both the allocation
problem, which asks for a welfare-maximizing partition and the decision
problem, which asks whether or not there exists a partition guaranteeing
certain welfare, for binary XOS valuations. For interactive protocols with
communication, a tight 3/4-approximation is known for both
[Fei06,DS06].
For interactive protocols, the allocation problem is provably harder than the
decision problem: any solution to the allocation problem implies a solution to
the decision problem with one additional round and additional bits of
communication via a trivial reduction. Surprisingly, the allocation problem is
provably easier for simultaneous protocols. Specifically, we show:
1) There exists a simultaneous, randomized protocol with polynomial
communication that selects a partition whose expected welfare is at least
of the optimum. This matches the guarantee of the best interactive, randomized
protocol with polynomial communication.
2) For all , any simultaneous, randomized protocol that
decides whether the welfare of the optimal partition is or correctly with probability requires
exponential communication. This provides a separation between the attainable
approximation guarantees via interactive () versus simultaneous () protocols with polynomial communication.
In other words, this trivial reduction from decision to allocation problems
provably requires the extra round of communication
Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games
Additively separable hedonic games and fractional hedonic games have received
considerable attention. They are coalition forming games of selfish agents
based on their mutual preferences. Most of the work in the literature
characterizes the existence and structure of stable outcomes (i.e., partitions
in coalitions), assuming that preferences are given. However, there is little
discussion on this assumption. In fact, agents receive different utilities if
they belong to different partitions, and thus it is natural for them to declare
their preferences strategically in order to maximize their benefit. In this
paper we consider strategyproof mechanisms for additively separable hedonic
games and fractional hedonic games, that is, partitioning methods without
payments such that utility maximizing agents have no incentive to lie about
their true preferences. We focus on social welfare maximization and provide
several lower and upper bounds on the performance achievable by strategyproof
mechanisms for general and specific additive functions. In most of the cases we
provide tight or asymptotically tight results. All our mechanisms are simple
and can be computed in polynomial time. Moreover, all the lower bounds are
unconditional, that is, they do not rely on any computational or complexity
assumptions
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