3,077 research outputs found
Optimal Auctions vs. Anonymous Pricing
For selling a single item to agents with independent but non-identically
distributed values, the revenue optimal auction is complex. With respect to it,
Hartline and Roughgarden (2009) showed that the approximation factor of the
second-price auction with an anonymous reserve is between two and four. We
consider the more demanding problem of approximating the revenue of the ex ante
relaxation of the auction problem by posting an anonymous price (while supplies
last) and prove that their worst-case ratio is e. As a corollary, the
upper-bound of anonymous pricing or anonymous reserves versus the optimal
auction improves from four to . We conclude that, up to an factor,
discrimination and simultaneity are unimportant for driving revenue in
single-item auctions.Comment: 19 pages, 6 figures, To appear in 56th Annual IEEE Symposium on
Foundations of Computer Science (FOCS 2015
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
Lower Bounds on Revenue of Approximately Optimal Auctions
We obtain revenue guarantees for the simple pricing mechanism of a single
posted price, in terms of a natural parameter of the distribution of buyers'
valuations. Our revenue guarantee applies to the single item n buyers setting,
with values drawn from an arbitrary joint distribution. Specifically, we show
that a single price drawn from the distribution of the maximum valuation Vmax =
max {V_1, V_2, ...,V_n} achieves a revenue of at least a 1/e fraction of the
geometric expecation of Vmax. This generic bound is a measure of how revenue
improves/degrades as a function of the concentration/spread of Vmax.
We further show that in absence of buyers' valuation distributions,
recruiting an additional set of identical bidders will yield a similar
guarantee on revenue. Finally, our bound also gives a measure of the extent to
which one can simultaneously approximate welfare and revenue in terms of the
concentration/spread of Vmax.Comment: The 8th Workshop on Internet and Network Economics (WINE
Vickrey Auctions for Irregular Distributions
The classic result of Bulow and Klemperer \cite{BK96} says that in a
single-item auction recruiting one more bidder and running the Vickrey auction
achieves a higher revenue than the optimal auction's revenue on the original
set of bidders, when values are drawn i.i.d. from a regular distribution. We
give a version of Bulow and Klemperer's result in settings where bidders'
values are drawn from non-i.i.d. irregular distributions. We do this by
modeling irregular distributions as some convex combination of regular
distributions. The regular distributions that constitute the irregular
distribution correspond to different population groups in the bidder
population. Drawing a bidder from this collection of population groups is
equivalent to drawing from some convex combination of these regular
distributions. We show that recruiting one extra bidder from each underlying
population group and running the Vickrey auction gives at least half of the
optimal auction's revenue on the original set of bidders
Chain: A Dynamic Double Auction Framework for Matching Patient Agents
In this paper we present and evaluate a general framework for the design of
truthful auctions for matching agents in a dynamic, two-sided market. A single
commodity, such as a resource or a task, is bought and sold by multiple buyers
and sellers that arrive and depart over time. Our algorithm, Chain, provides
the first framework that allows a truthful dynamic double auction (DA) to be
constructed from a truthful, single-period (i.e. static) double-auction rule.
The pricing and matching method of the Chain construction is unique amongst
dynamic-auction rules that adopt the same building block. We examine
experimentally the allocative efficiency of Chain when instantiated on various
single-period rules, including the canonical McAfee double-auction rule. For a
baseline we also consider non-truthful double auctions populated with
zero-intelligence plus"-style learning agents. Chain-based auctions perform
well in comparison with other schemes, especially as arrival intensity falls
and agent valuations become more volatile
Tight Revenue Gaps among Multi-Unit Mechanisms
This paper considers Bayesian revenue maximization in the -unit setting,
where a monopolist seller has copies of an indivisible item and faces
unit-demand buyers (whose value distributions can be non-identical). Four basic
mechanisms among others have been widely employed in practice and widely
studied in the literature: {\sf Myerson Auction}, {\sf Sequential
Posted-Pricing}, {\sf -th Price Auction with Anonymous Reserve}, and
{\sf Anonymous Pricing}. Regarding a pair of mechanisms, we investigate the
largest possible ratio between the two revenues (a.k.a.\ the revenue gap), over
all possible value distributions of the buyers.
Divide these four mechanisms into two groups: (i)~the discriminating
mechanism group, {\sf Myerson Auction} and {\sf Sequential Posted-Pricing}, and
(ii)~the anonymous mechanism group, {\sf Anonymous Reserve} and {\sf Anonymous
Pricing}. Within one group, the involved two mechanisms have an asymptotically
tight revenue gap of . In contrast, any two
mechanisms from the different groups have an asymptotically tight revenue gap
of
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