4,017 research outputs found
Optimal Competitive Auctions
We study the design of truthful auctions for selling identical items in
unlimited supply (e.g., digital goods) to n unit demand buyers. This classic
problem stands out from profit-maximizing auction design literature as it
requires no probabilistic assumptions on buyers' valuations and employs the
framework of competitive analysis. Our objective is to optimize the worst-case
performance of an auction, measured by the ratio between a given benchmark and
revenue generated by the auction.
We establish a sufficient and necessary condition that characterizes
competitive ratios for all monotone benchmarks. The characterization identifies
the worst-case distribution of instances and reveals intrinsic relations
between competitive ratios and benchmarks in the competitive analysis. With the
characterization at hand, we show optimal competitive auctions for two natural
benchmarks.
The most well-studied benchmark measures the
envy-free optimal revenue where at least two buyers win. Goldberg et al. [13]
showed a sequence of lower bounds on the competitive ratio for each number of
buyers n. They conjectured that all these bounds are tight. We show that
optimal competitive auctions match these bounds. Thus, we confirm the
conjecture and settle a central open problem in the design of digital goods
auctions. As one more application we examine another economically meaningful
benchmark, which measures the optimal revenue across all limited-supply Vickrey
auctions. We identify the optimal competitive ratios to be
for each number of buyers n, that is as
approaches infinity
Envy Freedom and Prior-free Mechanism Design
We consider the provision of an abstract service to single-dimensional
agents. Our model includes position auctions, single-minded combinatorial
auctions, and constrained matching markets. When the agents' values are drawn
from a distribution, the Bayesian optimal mechanism is given by Myerson (1981)
as a virtual-surplus optimizer. We develop a framework for prior-free mechanism
design and analysis. A good mechanism in our framework approximates the optimal
mechanism for the distribution if there is a distribution; moreover, when there
is no distribution this mechanism still performs well.
We define and characterize optimal envy-free outcomes in symmetric
single-dimensional environments. Our characterization mirrors Myerson's theory.
Furthermore, unlike in mechanism design where there is no point-wise optimal
mechanism, there is always a point-wise optimal envy-free outcome.
Envy-free outcomes and incentive-compatible mechanisms are similar in
structure and performance. We therefore use the optimal envy-free revenue as a
benchmark for measuring the performance of a prior-free mechanism. A good
mechanism is one that approximates the envy free benchmark on any profile of
agent values. We show that good mechanisms exist, and in particular, a natural
generalization of the random sampling auction of Goldberg et al. (2001) is a
constant approximation
Constant-Competitive Prior-Free Auction with Ordered Bidders
A central problem in Microeconomics is to design auctions with good revenue
properties. In this setting, the bidders' valuations for the items are private
knowledge, but they are drawn from publicly known prior distributions. The goal
is to find a truthful auction (no bidder can gain in utility by misreporting
her valuation) that maximizes the expected revenue.
Naturally, the optimal-auction is sensitive to the prior distributions. An
intriguing question is to design a truthful auction that is oblivious to these
priors, and yet manages to get a constant factor of the optimal revenue. Such
auctions are called prior-free.
Goldberg et al. presented a constant-approximate prior-free auction when
there are identical copies of an item available in unlimited supply, bidders
are unit-demand, and their valuations are drawn from i.i.d. distributions. The
recent work of Leonardi et al. [STOC 2012] generalized this problem to non
i.i.d. bidders, assuming that the auctioneer knows the ordering of their
reserve prices. Leonardi et al. proposed a prior-free auction that achieves a
approximation. We improve upon this result, by giving the first
prior-free auction with constant approximation guarantee.Comment: The same result has been obtained independently by E. Koutsoupias, S.
Leonardi and T. Roughgarde
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