37 research outputs found
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
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
Characterization of revenue equivalence
The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called \emph{revenue equivalence}. In this paper we give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent
Interdependent Public Projects
In the interdependent values (IDV) model introduced by Milgrom and Weber
[1982], agents have private signals that capture their information about
different social alternatives, and the valuation of every agent is a function
of all agent signals. While interdependence has been mainly studied for
auctions, it is extremely relevant for a large variety of social choice
settings, including the canonical setting of public projects. The IDV model is
very challenging relative to standard independent private values, and welfare
guarantees have been achieved through two alternative conditions known as {\em
single-crossing} and {\em submodularity over signals (SOS)}. In either case,
the existing theory falls short of solving the public projects setting.
Our contribution is twofold: (i) We give a workable characterization of
truthfulness for IDV public projects for the largest class of valuations for
which such a characterization exists, and term this class \emph{decomposable
valuations}; (ii) We provide possibility and impossibility results for welfare
approximation in public projects with SOS valuations. Our main impossibility
result is that, in contrast to auctions, no universally truthful mechanism
performs better for public projects with SOS valuations than choosing a project
at random. Our main positive result applies to {\em excludable} public projects
with SOS, for which we establish a constant factor approximation similar to
auctions. Our results suggest that exclusion may be a key tool for achieving
welfare guarantees in the IDV model
Optimal Competitive Auctions
We study the design of truthful auctions for selling identical items in
unlimited supply (e.g., digital goods) to n unit demand buyers. This classic
problem stands out from profit-maximizing auction design literature as it
requires no probabilistic assumptions on buyers' valuations and employs the
framework of competitive analysis. Our objective is to optimize the worst-case
performance of an auction, measured by the ratio between a given benchmark and
revenue generated by the auction.
We establish a sufficient and necessary condition that characterizes
competitive ratios for all monotone benchmarks. The characterization identifies
the worst-case distribution of instances and reveals intrinsic relations
between competitive ratios and benchmarks in the competitive analysis. With the
characterization at hand, we show optimal competitive auctions for two natural
benchmarks.
The most well-studied benchmark measures the
envy-free optimal revenue where at least two buyers win. Goldberg et al. [13]
showed a sequence of lower bounds on the competitive ratio for each number of
buyers n. They conjectured that all these bounds are tight. We show that
optimal competitive auctions match these bounds. Thus, we confirm the
conjecture and settle a central open problem in the design of digital goods
auctions. As one more application we examine another economically meaningful
benchmark, which measures the optimal revenue across all limited-supply Vickrey
auctions. We identify the optimal competitive ratios to be
for each number of buyers n, that is as
approaches infinity
New bounds for truthful scheduling on two unrelated selfish machines
We consider the minimum makespan problem for tasks and two unrelated
parallel selfish machines. Let be the best approximation ratio of
randomized monotone scale-free algorithms. This class contains the most
efficient algorithms known for truthful scheduling on two machines. We propose
a new formulation for , as well as upper and lower bounds on
based on this formulation. For the lower bound, we exploit pointwise
approximations of cumulative distribution functions (CDFs). For the upper
bound, we construct randomized algorithms using distributions with piecewise
rational CDFs. Our method improves upon the existing bounds on for small
. In particular, we obtain almost tight bounds for showing that
.Comment: 28 pages, 3 tables, 1 figure. Theory Comput Syst (2019