37 research outputs found
On Revenue Monotonicity in Combinatorial Auctions
Along with substantial progress made recently in designing near-optimal
mechanisms for multi-item auctions, interesting structural questions have also
been raised and studied. In particular, is it true that the seller can always
extract more revenue from a market where the buyers value the items higher than
another market? In this paper we obtain such a revenue monotonicity result in a
general setting. Precisely, consider the revenue-maximizing combinatorial
auction for items and buyers in the Bayesian setting, specified by a
valuation function and a set of independent item-type
distributions. Let denote the maximum revenue achievable under
by any incentive compatible mechanism. Intuitively, one would expect that
if distribution stochastically dominates .
Surprisingly, Hart and Reny (2012) showed that this is not always true even for
the simple case when is additive. A natural question arises: Are these
deviations contained within bounds? To what extent may the monotonicity
intuition still be valid? We present an {approximate monotonicity} theorem for
the class of fractionally subadditive (XOS) valuation functions , showing
that if stochastically dominates under
where is a universal constant. Previously, approximate monotonicity was
known only for the case : Babaioff et al. (2014) for the class of additive
valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation
functions.Comment: 10 page
Maximizing System Throughput Using Cooperative Sensing in Multi-Channel Cognitive Radio Networks
In Cognitive Radio Networks (CRNs), unlicensed users are allowed to access
the licensed spectrum when it is not currently being used by primary users
(PUs). In this paper, we study the throughput maximization problem for a
multi-channel CRN where each SU can only sense a limited number of channels. We
show that this problem is strongly NP-hard, and propose an approximation
algorithm with a factor at least where is a system
parameter reflecting the sensing capability of SUs across channels and their
sensing budgets. This performance guarantee is achieved by exploiting a nice
structural property of the objective function and constructing a particular
matching. Our numerical results demonstrate the advantage of our algorithm
compared with both a random and a greedy sensing assignment algorithm
Single Parameter Combinatorial Auctions with Partially Public Valuations
We consider the problem of designing truthful auctions, when the bidders'
valuations have a public and a private component. In particular, we consider
combinatorial auctions where the valuation of an agent for a set of
items can be expressed as , where is a private single parameter
of the agent, and the function is publicly known. Our motivation behind
studying this problem is two-fold: (a) Such valuation functions arise naturally
in the case of ad-slots in broadcast media such as Television and Radio. For an
ad shown in a set of ad-slots, is, say, the number of {\em unique}
viewers reached by the ad, and is the valuation per-unique-viewer. (b)
From a theoretical point of view, this factorization of the valuation function
simplifies the bidding language, and renders the combinatorial auction more
amenable to better approximation factors. We present a general technique, based
on maximal-in-range mechanisms, that converts any -approximation
non-truthful algorithm () for this problem into
and -approximate truthful
mechanisms which run in polynomial time and quasi-polynomial time,
respectively
Enabling Privacy-preserving Auctions in Big Data
We study how to enable auctions in the big data context to solve many
upcoming data-based decision problems in the near future. We consider the
characteristics of the big data including, but not limited to, velocity,
volume, variety, and veracity, and we believe any auction mechanism design in
the future should take the following factors into consideration: 1) generality
(variety); 2) efficiency and scalability (velocity and volume); 3) truthfulness
and verifiability (veracity). In this paper, we propose a privacy-preserving
construction for auction mechanism design in the big data, which prevents
adversaries from learning unnecessary information except those implied in the
valid output of the auction. More specifically, we considered one of the most
general form of the auction (to deal with the variety), and greatly improved
the the efficiency and scalability by approximating the NP-hard problems and
avoiding the design based on garbled circuits (to deal with velocity and
volume), and finally prevented stakeholders from lying to each other for their
own benefit (to deal with the veracity). We achieve these by introducing a
novel privacy-preserving winner determination algorithm and a novel payment
mechanism. Additionally, we further employ a blind signature scheme as a
building block to let bidders verify the authenticity of their payment reported
by the auctioneer. The comparison with peer work shows that we improve the
asymptotic performance of peer works' overhead from the exponential growth to a
linear growth and from linear growth to a logarithmic growth, which greatly
improves the scalability
Bayesian Incentive Compatibility via Fractional Assignments
Very recently, Hartline and Lucier studied single-parameter mechanism design
problems in the Bayesian setting. They proposed a black-box reduction that
converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible
(BIC) mechanisms while preserving social welfare. It remains a major open
question if one can find similar reduction in the more important
multi-parameter setting. In this paper, we give positive answer to this
question when the prior distribution has finite and small support. We propose a
black-box reduction for designing BIC multi-parameter mechanisms. The reduction
converts any algorithm into an eps-BIC mechanism with only marginal loss in
social welfare. As a result, for combinatorial auctions with sub-additive
agents we get an eps-BIC mechanism that achieves constant approximation.Comment: 22 pages, 1 figur
Prophet Secretary for Combinatorial Auctions and Matroids
The secretary and the prophet inequality problems are central to the field of
Stopping Theory. Recently, there has been a lot of work in generalizing these
models to multiple items because of their applications in mechanism design. The
most important of these generalizations are to matroids and to combinatorial
auctions (extends bipartite matching). Kleinberg-Weinberg \cite{KW-STOC12} and
Feldman et al. \cite{feldman2015combinatorial} show that for adversarial
arrival order of random variables the optimal prophet inequalities give a
-approximation. For many settings, however, it's conceivable that the
arrival order is chosen uniformly at random, akin to the secretary problem. For
such a random arrival model, we improve upon the -approximation and obtain
-approximation prophet inequalities for both matroids and
combinatorial auctions. This also gives improvements to the results of Yan
\cite{yan2011mechanism} and Esfandiari et al. \cite{esfandiari2015prophet} who
worked in the special cases where we can fully control the arrival order or
when there is only a single item.
Our techniques are threshold based. We convert our discrete problem into a
continuous setting and then give a generic template on how to dynamically
adjust these thresholds to lower bound the expected total welfare.Comment: Preliminary version appeared in SODA 2018. This version improves the
writeup on Fixed-Threshold algorithm