9 research outputs found
Rate of Price Discovery in Iterative Combinatorial Auctions
We study a class of iterative combinatorial auctions which can be viewed as
subgradient descent methods for the problem of pricing bundles to balance
supply and demand. We provide concrete convergence rates for auctions in this
class, bounding the number of auction rounds needed to reach clearing prices.
Our analysis allows for a variety of pricing schemes, including item, bundle,
and polynomial pricing, and the respective convergence rates confirm that more
expressive pricing schemes come at the cost of slower convergence. We consider
two models of bidder behavior. In the first model, bidders behave
stochastically according to a random utility model, which includes standard
best-response bidding as a special case. In the second model, bidders behave
arbitrarily (even adversarially), and meaningful convergence relies on properly
designed activity rules
A Scalable Neural Network for DSIC Affine Maximizer Auction Design
Automated auction design aims to find empirically high-revenue mechanisms
through machine learning. Existing works on multi item auction scenarios can be
roughly divided into RegretNet-like and affine maximizer auctions (AMAs)
approaches. However, the former cannot strictly ensure dominant strategy
incentive compatibility (DSIC), while the latter faces scalability issue due to
the large number of allocation candidates. To address these limitations, we
propose AMenuNet, a scalable neural network that constructs the AMA parameters
(even including the allocation menu) from bidder and item representations.
AMenuNet is always DSIC and individually rational (IR) due to the properties of
AMAs, and it enhances scalability by generating candidate allocations through a
neural network. Additionally, AMenuNet is permutation equivariant, and its
number of parameters is independent of auction scale. We conduct extensive
experiments to demonstrate that AMenuNet outperforms strong baselines in both
contextual and non-contextual multi-item auctions, scales well to larger
auctions, generalizes well to different settings, and identifies useful
deterministic allocations. Overall, our proposed approach offers an effective
solution to automated DSIC auction design, with improved scalability and strong
revenue performance in various settings.Comment: NeurIPS 2023 (spotlight
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
Truthful and Fair Resource Allocation
How should we divide a good or set of goods among a set of agents? There are various constraints that we can consider. We consider two particular constraints. The first is fairness - how can we find fair allocations? The second is truthfulness - what if we do not know agents valuations for the goods being allocated? What if these valuations need to be elicited, and agents will misreport their valuations if it is beneficial? Can we design procedures that elicit agents' true valuations while preserving the quality of the allocation? We consider truthful and fair resource allocation procedures through a computational lens. We first study fair division of a heterogeneous, divisible good, colloquially known as the cake cutting problem. We depart from the existing literature and assume that agents have restricted valuations that can be succinctly communicated. We consider the problems of welfare-maximization, expressiveness, and truthfulness in cake cutting under this model. In the second part of this dissertation we consider truthfulness in settings where payments can be used to incentivize agents to truthfully reveal their private information. A mechanism asks agents to report their private preference information and computes an allocation and payments based on these reports. The mechanism design problem is to find incentive compatible mechanisms which incentivize agents to truthfully reveal their private information and simultaneously compute allocations with desirable properties. The traditional approach to mechanism design specifies mechanisms by hand and proves that certain desirable properties are satisfied. This limits the design space to mechanisms that can be written down and analyzed. We take a computational approach, giving computational procedures that produce mechanisms with desirable properties. Our first contribution designs a procedure that modifies heuristic branch and bound search and makes it usable as the allocation algorithm in an incentive compatible mechanism. Our second contribution draws a novel connection between incentive compatible mechanisms and machine learning. We use this connection to learn payment rules to pair with provided allocation rules. Our payment rules are not exactly incentive compatibility, but they minimize a measure of how much agents can gain by misreporting.Engineering and Applied Science
A Kernel-Based Iterative Combinatorial Auction
This paper describes an iterative combinatorial auction for single-minded bidders that offers modularity in the choice of price structure, drawing on ideas from kernel methods and the primal-dual paradigm of auction design. In our implementation, the auction is able to automatically detect, as the rounds progress, whether price expressiveness must be increased to clear the market. The auction also features a configurable step size which can be tuned to trade-off between monotonicity in prices and the number of bidding rounds, with no impact on efficiency. An empirical evaluation against a state of the art ascending-price auction demonstrates the performance gains that can be obtained in efficiency, revenue, and rounds to convergence through various configurations of our design