3 research outputs found
Optimal (and Benchmark-Optimal) Competition Complexity for Additive Buyers over Independent Items
The Competition Complexity of an auction setting refers to the number of
additional bidders necessary in order for the (deterministic,
prior-independent, dominant strategy truthful) Vickrey-Clarke-Groves mechanism
to achieve greater revenue than the (randomized, prior-dependent,
Bayesian-truthful) optimal mechanism without the additional bidders.
We prove that the competition complexity of bidders with additive
valuations over independent items is at most , and also at
most . When , the first bound is optimal up to constant
factors, even when the items are i.i.d. and regular. When , the
second bound is optimal for the benchmark introduced in [EFFTW17a] up to
constant factors, even when the items are i.i.d. and regular. We further show
that, while the Eden et al. benchmark is not necessarily tight in the regime, the competition complexity of bidders with additive valuations
over even i.i.d. regular items is indeed .
Our main technical contribution is a reduction from analyzing the Eden et al.
benchmark to proving stochastic dominance of certain random variables
A Permutation-Equivariant Neural Network Architecture For Auction Design
Designing an incentive compatible auction that maximizes expected revenue is
a central problem in Auction Design. Theoretical approaches to the problem have
hit some limits in the past decades and analytical solutions are known for only
a few simple settings. Computational approaches to the problem through the use
of LPs have their own set of limitations. Building on the success of deep
learning, a new approach was recently proposed by Duetting et al. (2019) in
which the auction is modeled by a feed-forward neural network and the design
problem is framed as a learning problem. The neural architectures used in that
work are general purpose and do not take advantage of any of the symmetries the
problem could present, such as permutation equivariance. In this work, we
consider auction design problems that have permutation-equivariant symmetry and
construct a neural architecture that is capable of perfectly recovering the
permutation-equivariant optimal mechanism, which we show is not possible with
the previous architecture. We demonstrate that permutation-equivariant
architectures are not only capable of recovering previous results, they also
have better generalization properties