6,232 research outputs found
Pricing for Online Resource Allocation: Intervals and Paths
We present pricing mechanisms for several online resource allocation problems
which obtain tight or nearly tight approximations to social welfare. In our
settings, buyers arrive online and purchase bundles of items; buyers' values
for the bundles are drawn from known distributions. This problem is closely
related to the so-called prophet-inequality of Krengel and Sucheston and its
extensions in recent literature. Motivated by applications to cloud economics,
we consider two kinds of buyer preferences. In the first, items correspond to
different units of time at which a resource is available; the items are
arranged in a total order and buyers desire intervals of items. The second
corresponds to bandwidth allocation over a tree network; the items are edges in
the network and buyers desire paths.
Because buyers' preferences have complementarities in the settings we
consider, recent constant-factor approximations via item prices do not apply,
and indeed strong negative results are known. We develop static, anonymous
bundle pricing mechanisms.
For the interval preferences setting, we show that static, anonymous bundle
pricings achieve a sublogarithmic competitive ratio, which is optimal (within
constant factors) over the class of all online allocation algorithms, truthful
or not. For the path preferences setting, we obtain a nearly-tight logarithmic
competitive ratio. Both of these results exhibit an exponential improvement
over item pricings for these settings. Our results extend to settings where the
seller has multiple copies of each item, with the competitive ratio decreasing
linearly with supply. Such a gradual tradeoff between supply and the
competitive ratio for welfare was previously known only for the single item
prophet inequality
Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms
We study revenue maximization through sequential posted-price (SPP)
mechanisms in single-dimensional settings with buyers and independent but
not necessarily identical value distributions. We construct the SPP mechanisms
by considering the best of two simple pricing rules: one that imitates the
revenue optimal mchanism, namely the Myersonian mechanism, via the taxation
principle and the other that posts a uniform price. Our pricing rules are
rather generalizable and yield the first improvement over long-established
approximation factors in several settings. We design factor-revealing
mathematical programs that crisply capture the approximation factor of our SPP
mechanism. In the single-unit setting, our SPP mechanism yields a better
approximation factor than the state of the art prior to our work (Azar,
Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields
the first improved approximation factor over the state of the art after over
nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP
mechanisms immediately imply improved performance guarantees for the equivalent
free-order prophet inequality problem. In the position auction setting, our SPP
mechanism yields the first higher-than approximation factor. In eager
second-price (ESP) auctions, our two simple pricing rules lead to the first
improved approximation factor that is strictly greater than what is obtained by
the SPP mechanism in the single-unit setting.Comment: Accepted to Operations Researc
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
Pricing Multi-Unit Markets
We study the power and limitations of posted prices in multi-unit markets,
where agents arrive sequentially in an arbitrary order. We prove upper and
lower bounds on the largest fraction of the optimal social welfare that can be
guaranteed with posted prices, under a range of assumptions about the
designer's information and agents' valuations. Our results provide insights
about the relative power of uniform and non-uniform prices, the relative
difficulty of different valuation classes, and the implications of different
informational assumptions. Among other results, we prove constant-factor
guarantees for agents with (symmetric) subadditive valuations, even in an
incomplete-information setting and with uniform prices
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