2,370 research outputs found
Sampling and Representation Complexity of Revenue Maximization
We consider (approximate) revenue maximization in auctions where the
distribution on input valuations is given via "black box" access to samples
from the distribution. We observe that the number of samples required -- the
sample complexity -- is tightly related to the representation complexity of an
approximately revenue-maximizing auction. Our main results are upper bounds and
an exponential lower bound on these complexities
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
Coverage, Matching, and Beyond: New Results on Budgeted Mechanism Design
We study a type of reverse (procurement) auction problems in the presence of
budget constraints. The general algorithmic problem is to purchase a set of
resources, which come at a cost, so as not to exceed a given budget and at the
same time maximize a given valuation function. This framework captures the
budgeted version of several well known optimization problems, and when the
resources are owned by strategic agents the goal is to design truthful and
budget feasible mechanisms, i.e. elicit the true cost of the resources and
ensure the payments of the mechanism do not exceed the budget. Budget
feasibility introduces more challenges in mechanism design, and we study
instantiations of this problem for certain classes of submodular and XOS
valuation functions. We first obtain mechanisms with an improved approximation
ratio for weighted coverage valuations, a special class of submodular functions
that has already attracted attention in previous works. We then provide a
general scheme for designing randomized and deterministic polynomial time
mechanisms for a class of XOS problems. This class contains problems whose
feasible set forms an independence system (a more general structure than
matroids), and some representative problems include, among others, finding
maximum weighted matchings, maximum weighted matroid members, and maximum
weighted 3D-matchings. For most of these problems, only randomized mechanisms
with very high approximation ratios were known prior to our results
Efficiency Guarantees in Auctions with Budgets
In settings where players have a limited access to liquidity, represented in
the form of budget constraints, efficiency maximization has proven to be a
challenging goal. In particular, the social welfare cannot be approximated by a
better factor then the number of players. Therefore, the literature has mainly
resorted to Pareto-efficiency as a way to achieve efficiency in such settings.
While successful in some important scenarios, in many settings it is known that
either exactly one incentive-compatible auction that always outputs a
Pareto-efficient solution, or that no truthful mechanism can always guarantee a
Pareto-efficient outcome. Traditionally, impossibility results can be avoided
by considering approximations. However, Pareto-efficiency is a binary property
(is either satisfied or not), which does not allow for approximations.
In this paper we propose a new notion of efficiency, called \emph{liquid
welfare}. This is the maximum amount of revenue an omniscient seller would be
able to extract from a certain instance. We explain the intuition behind this
objective function and show that it can be 2-approximated by two different
auctions. Moreover, we show that no truthful algorithm can guarantee an
approximation factor better than 4/3 with respect to the liquid welfare, and
provide a truthful auction that attains this bound in a special case.
Importantly, the liquid welfare benchmark also overcomes impossibilities for
some settings. While it is impossible to design Pareto-efficient auctions for
multi-unit auctions where players have decreasing marginal values, we give a
deterministic -approximation for the liquid welfare in this setting
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
Social Dilemmas and Cooperation in Complex Networks
In this paper we extend the investigation of cooperation in some classical
evolutionary games on populations were the network of interactions among
individuals is of the scale-free type. We show that the update rule, the payoff
computation and, to some extent the timing of the operations, have a marked
influence on the transient dynamics and on the amount of cooperation that can
be established at equilibrium. We also study the dynamical behavior of the
populations and their evolutionary stability.Comment: 12 pages, 7 figures. to appea
Randomized Revenue Monotone Mechanisms for Online Advertising
Online advertising is the main source of revenue for many Internet firms. A
central component of online advertising is the underlying mechanism that
selects and prices the winning ads for a given ad slot. In this paper we study
designing a mechanism for the Combinatorial Auction with Identical Items (CAII)
in which we are interested in selling identical items to a group of bidders
each demanding a certain number of items between and . CAII generalizes
important online advertising scenarios such as image-text and video-pod
auctions [GK14]. In image-text auction we want to fill an advertising slot on a
publisher's web page with either text-ads or a single image-ad and in
video-pod auction we want to fill an advertising break of seconds with
video-ads of possibly different durations.
Our goal is to design truthful mechanisms that satisfy Revenue Monotonicity
(RM). RM is a natural constraint which states that the revenue of a mechanism
should not decrease if the number of participants increases or if a participant
increases her bid.
[GK14] showed that no deterministic RM mechanism can attain PoRM of less than
for CAII, i.e., no deterministic mechanism can attain more than
fraction of the maximum social welfare. [GK14] also design a
mechanism with PoRM of for CAII.
In this paper, we seek to overcome the impossibility result of [GK14] for
deterministic mechanisms by using the power of randomization. We show that by
using randomization, one can attain a constant PoRM. In particular, we design a
randomized RM mechanism with PoRM of for CAII
Experimental realization of a quantum game on a one-way quantum computer
We report the first demonstration of a quantum game on an all-optical one-way
quantum computer. Following a recent theoretical proposal we implement a
quantum version of Prisoner's Dilemma, where the quantum circuit is realized by
a 4-qubit box-cluster configuration and the player's local strategies by
measurements performed on the physical qubits of the cluster. This
demonstration underlines the strength and versatility of the one-way model and
we expect that this will trigger further interest in designing quantum
protocols and algorithms to be tested in state-of-the-art cluster resources.Comment: 13 pages, 4 figure
Quantum Games and Quantum Strategies
We investigate the quantization of non-zero sum games. For the particular
case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma
if quantum strategies are allowed for. We also construct a particular quantum
strategy which always gives reward if played against any classical strategy.Comment: 4 pages, 4 figures, typographic sign error in the definition of the
operator J correcte
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
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