1,325 research outputs found
A deterministic truthful PTAS for scheduling related machines
Scheduling on related machines () is one of the most important
problems in the field of Algorithmic Mechanism Design. Each machine is
controlled by a selfish agent and her valuation can be expressed via a single
parameter, her {\em speed}. In contrast to other similar problems, Archer and
Tardos \cite{AT01} showed that an algorithm that minimizes the makespan can be
truthfully implemented, although in exponential time. On the other hand, if we
leave out the game-theoretic issues, the complexity of the problem has been
completely settled -- the problem is strongly NP-hard, while there exists a
PTAS \cite{HS88,ES04}.
This problem is the most well studied in single-parameter algorithmic
mechanism design. It gives an excellent ground to explore the boundary between
truthfulness and efficient computation. Since the work of Archer and Tardos,
quite a lot of deterministic and randomized mechanisms have been suggested.
Recently, a breakthrough result \cite{DDDR08} showed that a randomized truthful
PTAS exists. On the other hand, for the deterministic case, the best known
approximation factor is 2.8 \cite{Kov05,Kov07}.
It has been a major open question whether there exists a deterministic
truthful PTAS, or whether truthfulness has an essential, negative impact on the
computational complexity of the problem. In this paper we give a definitive
answer to this important question by providing a truthful {\em deterministic}
PTAS
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources
We study the efficiency of the proportional allocation mechanism, that is
widely used to allocate divisible resources. Each agent submits a bid for each
divisible resource and receives a fraction proportional to her bids. We
quantify the inefficiency of Nash equilibria by studying the Price of Anarchy
(PoA) of the induced game under complete and incomplete information. When
agents' valuations are concave, we show that the Bayesian Nash equilibria can
be arbitrarily inefficient, in contrast to the well-known 4/3 bound for pure
equilibria. Next, we upper bound the PoA over Bayesian equilibria by 2 when
agents' valuations are subadditive, generalizing and strengthening previous
bounds on lattice submodular valuations. Furthermore, we show that this bound
is tight and cannot be improved by any simple or scale-free mechanism. Then we
switch to settings with budget constraints, and we show an improved upper bound
on the PoA over coarse-correlated equilibria. Finally, we prove that the PoA is
exactly 2 for pure equilibria in the polyhedral environment.Comment: To appear in SAGT 201
Tight Bounds for the Price of Anarchy of Simultaneous First Price Auctions
We study the Price of Anarchy of simultaneous first-price auctions for buyers
with submodular and subadditive valuations. The current best upper bounds for
the Bayesian Price of Anarchy of these auctions are e/(e-1) [Syrgkanis and
Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching
lower bounds for both cases even for the case of full information and for mixed
Nash equilibria via an explicit construction.
We present an alternative proof of the upper bound of e/(e-1) for first-price
auctions with fractionally subadditive valuations which reveals the worst-case
price distribution, that is used as a building block for the matching lower
bound construction.
We generalize our results to a general class of item bidding auctions that we
call bid-dependent auctions (including first-price auctions and all-pay
auctions) where the winner is always the highest bidder and each bidder's
payment depends only on his own bid.
Finally, we apply our techniques to discriminatory price multi-unit auctions.
We complement the results of [de Keijzer et al. 2013] for the case of
subadditive valuations, by providing a matching lower bound of 2. For the case
of submodular valuations, we provide a lower bound of 1.109. For the same class
of valuations, we were able to reproduce the upper bound of e/(e-1) using our
non-smooth approach.Comment: 37 pages, 5 figures, ACM Transactions on Economics and Computatio
Groundwater investigation in Paphos region
Cyprus is a semi-arid island. Its water resources rely on winter
rainfall which supply the impounding reservoirs constructed on the dry
river courses and replenish the groundwater resources within the river
gravels or the plain aquifers.
water requirements for domestic use and irrigation have been
increasing considerably for the last ten years. The potential of the
conventional water resources have been developed according to techno-economic
factors. Also, the unconventional sources (treated domestic
effluents and desalinating sea water) are receiving particular
attention to support water requirements throughout the island.
The current study deals partly with the calcarenite aquifer of
the Paphos Coastal Plain. It has been investigated whether this
resource is offered for an integrated exploitation program. In
addition the domestic effluent of the Paphos urban zone is considered
as a promising resource for providing reliable and continuous
quantities for irrigation use after treatment. [Continues.
Truthful Allocation in Graphs and Hypergraphs
We study truthful mechanisms for allocation problems in graphs, both for the minimization (i.e., scheduling) and maximization (i.e., auctions) setting. The minimization problem is a special case of the well-studied unrelated machines scheduling problem, in which every given task can be executed only by two pre-specified machines in the case of graphs or a given subset of machines in the case of hypergraphs. This corresponds to a multigraph whose nodes are the machines and its hyperedges are the tasks. This class of problems belongs to multidimensional mechanism design, for which there are no known general mechanisms other than the VCG and its generalization to affine minimizers. We propose a new class of mechanisms that are truthful and have significantly better performance than affine minimizers in many settings. Specifically, we provide upper and lower bounds for truthful mechanisms for general multigraphs, as well as special classes of graphs such as stars, trees, planar graphs, k-degenerate graphs, and graphs of a given treewidth. We also consider the objective of minimizing or maximizing the L^p-norm of the values of the players, a generalization of the makespan minimization that corresponds to p = ?, and extend the results to any p > 0
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