9 research outputs found
Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility
The revenue optimal mechanism for selling a single item to agents with
independent but non-identically distributed values is complex for agents with
linear utility (Myerson,1981) and has no closed-form characterization for
agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for
linear utility agents satisfying a natural regularity property, Alaei et al.
(2018) showed that simply posting an anonymous price is an e-approximation. We
give a parameterization of the regularity property that extends to agents with
non-linear utility and show that the approximation bound of anonymous pricing
for regular agents approximately extends to agents that satisfy this
approximate regularity property. We apply this approximation framework to prove
that anonymous pricing is a constant approximation to the revenue optimal
single-item auction for agents with public-budget utility, private-budget
utility, and (a special case of) risk-averse utility.Comment: Appeared at EC 201
Third-degree Price Discrimination Versus Uniform Pricing
We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This revenue bound obtains for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight, and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons
Uniform Pricing Versus Third-Degree Price Discrimination
We compare the revenue of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave revenue functions and common support, a uniform price is guaranteed to achieve one-half of the optimal monopoly profits. This revenue bound holds for any arbitrary number of segments and prices that the seller would use in case he would engage in third-degree price discrimination. We further establish that these conditions are tight and that a weakening of common support or concavity leads to arbitrarily poor revenue comparisons
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
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
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Bayesian Auction Design and Approximation
We study two classes of problems within Algorithmic Economics: revenue guarantees of simple mechanisms, and social welfare guarantees of auctions. We develop new structural and algorithmic tools for addressing these problems, and obtain the following results:
In the -unit model, four canonical mechanisms can be classified as: (i) the discriminating group, including Myerson Auction and Sequential Posted-Pricing, and (ii) the anonymous group, including Anonymous Reserve and Anonymous Pricing. We prove that any two mechanisms from the same group have an asymptotically tight revenue gap of 1 + θ(1 /√), while any two mechanisms from the different groups have an asymptotically tight revenue gap of θ(log ).
In the single-item model, we prove a nearly-tight sample complexity of Anonymous Reserve for every value distribution family investigated in the literature: [0, 1]-bounded, [1, ]-bounded, regular, and monotone hazard rate (MHR).
Remarkably, the setting-specific sample complexity poly(⁻¹) depends on the precision ∈ (0, 1), but not on the number of bidders ≥ 1. Further, in the two bounded-support settings, our algorithm allows correlated value distributions. These are in sharp contrast to the previous (nearly-tight) sample complexity results on Myerson Auction.
In the single-item model, we prove that the tight Price of Anarchy/Stability for First Price Auctions are both PoA = PoS = 1 - 1/² ≈ 0.8647