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 $\mathcal{F}^{(2)}(\cdot)$ 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 $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ 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 $\alpha$-core-competitive if its revenue is at least $1/\alpha$ 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 $k$ text ads. We design an $O(\ln \ln k)$ core-competitive randomized auction and an $O(\sqrt{\ln(k)})$ 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