43,872 research outputs found
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
Core-competitive Auctions
One of the major drawbacks of the celebrated VCG auction is its low (or zero)
revenue even when the agents have high value for the goods and a {\em
competitive} outcome could have generated a significant revenue. A competitive
outcome is one for which it is impossible for the seller and a subset of buyers
to `block' the auction by defecting and negotiating an outcome with higher
payoffs for themselves. This corresponds to the well-known concept of {\em
core} in cooperative game theory.
In particular, VCG revenue is known to be not competitive when the goods
being sold have complementarities. A bottleneck here is an impossibility result
showing that there is no auction that simultaneously achieves competitive
prices (a core outcome) and incentive-compatibility.
In this paper we try to overcome the above impossibility result by asking the
following natural question: is it possible to design an incentive-compatible
auction whose revenue is comparable (even if less) to a competitive outcome?
Towards this, we define a notion of {\em core-competitive} auctions. We say
that an incentive-compatible auction is -core-competitive if its
revenue is at least fraction of the minimum revenue of a
core-outcome. We study the Text-and-Image setting. In this setting, there is an
ad slot which can be filled with either a single image ad or text ads. We
design an core-competitive randomized auction and an
competitive deterministic auction for the Text-and-Image
setting. We also show that both factors are tight
Middle Atmosphere Electrodynamics (MAE). Middle atmospheric electrodynamics during MAP
The recent revival and strong motivation for research in middle atmospheric electrodynamics can be attributed, in large part, to the discovery of large (V/m) electric fields within the lower mesosphere during the decade prior to MAP. Subsequent rocket soundings appeared to verify the preliminary findings. During the MAP era, more sophisticated techniques have been employed to obtain measurements which respond positively to criticisms of earlier results, and which provide more insight regarding the character of the fields. The occurrence of mesospheric V/m electric fields now seems to require the presence of aerosols, of local winds and related dynamics, and of an atmospheric electrical conductivity less than 10(-10)S/m. Furthermore, new theoretical ideas describing the origin of the V/m fields are consistent with the measurements. The current status of results regarding V/m fields in the middle atmosphere is reviewed in light of the more widely accepted electric field structure for this region from rocket, balloon and modeling results
Silicon ions below 100 km: A case for SiO2(+)
Silicon ions are normally detected at altitudes above 100 km and within sporadic E layers. Traces have rarely been observed within the more permanent metallic layer near 93 km. This is surprising since silicon is an important constituent of chondritic meteorites, which ablate material in this region to provide a primary source of the metallic species observed there. Evidence is presented that Si(+)ions form SiO2(+) at the lower altitudes, and exist in this ionic state prior to recombination. A rocket launched from El Arenosillo, Spain on 3 July 1972, at 0743 LMT, during the predicted period of the Beta Taurids meteor shower, passed through a continuous belt of metallic ions that began near 85 km, ended near 115 km, and exhibited an order of magnitude increase in the form of a layer near 114 km. Si(+)was measured in and below the ledge down to 103 km. It showed a rapid decrease below this height. Radiative association is offered as a primary mechanism for SiO2(+) production
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