14,724 research outputs found
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned
Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditional optimal mechanism design
approach is ill-suited --- either because it makes overly strong assumptions,
or because it advocates overly complex designs. The thesis of this paper is
that approximately optimal mechanisms allow us to reason about fundamental
questions that seem out of reach of the traditional theory.
This survey has three main parts. The first part describes the approximately
optimal mechanism design paradigm --- how it works, and what we aim to learn by
applying it. The second and third parts of the survey cover two case studies,
where we instantiate the general design paradigm to investigate two basic
questions. In the first example, we consider revenue maximization in a
single-item auction with heterogeneous bidders. Our goal is to understand if
complexity --- in the sense of detailed distributional knowledge --- is an
essential feature of good auctions for this problem, or alternatively if there
are simpler auctions that are near-optimal. The second example considers
welfare maximization with multiple items. Our goal here is similar in spirit:
when is complexity --- in the form of high-dimensional bid spaces --- an
essential feature of every auction that guarantees reasonable welfare? Are
there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on
Economics and Computation (EC), June 201
Learning Multi-item Auctions with (or without) Samples
We provide algorithms that learn simple auctions whose revenue is
approximately optimal in multi-item multi-bidder settings, for a wide range of
valuations including unit-demand, additive, constrained additive, XOS, and
subadditive. We obtain our learning results in two settings. The first is the
commonly studied setting where sample access to the bidders' distributions over
valuations is given, for both regular distributions and arbitrary distributions
with bounded support. Our algorithms require polynomially many samples in the
number of items and bidders. The second is a more general max-min learning
setting that we introduce, where we are given "approximate distributions," and
we seek to compute an auction whose revenue is approximately optimal
simultaneously for all "true distributions" that are close to the given ones.
These results are more general in that they imply the sample-based results, and
are also applicable in settings where we have no sample access to the
underlying distributions but have estimated them indirectly via market research
or by observation of previously run, potentially non-truthful auctions.
Our results hold for valuation distributions satisfying the standard (and
necessary) independence-across-items property. They also generalize and improve
upon recent works, which have provided algorithms that learn approximately
optimal auctions in more restricted settings with additive, subadditive and
unit-demand valuations using sample access to distributions. We generalize
these results to the complete unit-demand, additive, and XOS setting, to i.i.d.
subadditive bidders, and to the max-min setting.
Our results are enabled by new uniform convergence bounds for hypotheses
classes under product measures. Our bounds result in exponential savings in
sample complexity compared to bounds derived by bounding the VC dimension, and
are of independent interest.Comment: Appears in FOCS 201
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
The Value of Information Concealment
We consider a revenue optimizing seller selling a single item to a buyer, on
whose private value the seller has a noisy signal. We show that, when the
signal is kept private, arbitrarily more revenue could potentially be extracted
than if the signal is leaked or revealed. We then show that, if the seller is
not allowed to make payments to the buyer, the gap between the two is bounded
by a multiplicative factor of 3, if the value distribution conditioning on each
signal is regular. We give examples showing that both conditions are necessary
for a constant bound to hold.
We connect this scenario to multi-bidder single-item auctions where bidders'
values are correlated. Similarly to the setting above, we show that the revenue
of a Bayesian incentive compatible, ex post individually rational auction can
be arbitrarily larger than that of a dominant strategy incentive compatible
auction, whereas the two are no more than a factor of 5 apart if the auctioneer
never pays the bidders and if each bidder's value conditioning on the others'
is drawn according to a regular distribution. The upper bounds in both settings
degrade gracefully when the distribution is a mixture of a small number of
regular distributions
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