3 research outputs found
Learning Reserve Prices in Second-Price Auctions
This paper proves the tight sample complexity of Second-Price Auction with
Anonymous Reserve, up to a logarithmic factor, for all value distribution
families that have been considered in the literature. Compared to Myerson
Auction, whose sample complexity was settled very recently in (Guo, Huang and
Zhang, STOC 2019), Anonymous Reserve requires much fewer samples for learning.
We follow a similar framework as the Guo-Huang-Zhang work, but replace their
information theoretical argument with a direct proof
Robust Revenue Maximization Under Minimal Statistical Information
We study the problem of multi-dimensional revenue maximization when selling
items to a buyer that has additive valuations for them, drawn from a
(possibly correlated) prior distribution. Unlike traditional Bayesian auction
design, we assume that the seller has a very restricted knowledge of this
prior: they only know the mean and an upper bound on the
standard deviation of each item's marginal distribution. Our goal is to design
mechanisms that achieve good revenue against an ideal optimal auction that has
full knowledge of the distribution in advance. Informally, our main
contribution is a tight quantification of the interplay between the dispersity
of the priors and the aforementioned robust approximation ratio. Furthermore,
this can be achieved by very simple selling mechanisms.
More precisely, we show that selling the items via separate price lotteries
achieves an approximation ratio where is
the maximum coefficient of variation across the items. If forced to restrict
ourselves to deterministic mechanisms, this guarantee degrades to .
Assuming independence of the item valuations, these ratios can be further
improved by pricing the full bundle. For the case of identical means and
variances, in particular, we get a guarantee of which converges
to optimality as the number of items grows large. We demonstrate the optimality
of the above mechanisms by providing matching lower bounds. Our tight analysis
for the deterministic case resolves an open gap from the work of Azar and
Micali [ITCS'13].
As a by-product, we also show how one can directly use our upper bounds to
improve and extend previous results related to the parametric auctions of Azar
et al. [SODA'13]