385 research outputs found
Composable and Efficient Mechanisms
We initiate the study of efficient mechanism design with guaranteed good
properties even when players participate in multiple different mechanisms
simultaneously or sequentially. We define the class of smooth mechanisms,
related to smooth games defined by Roughgarden, that can be thought of as
mechanisms that generate approximately market clearing prices. We show that
smooth mechanisms result in high quality outcome in equilibrium both in the
full information setting and in the Bayesian setting with uncertainty about
participants, as well as in learning outcomes. Our main result is to show that
such mechanisms compose well: smoothness locally at each mechanism implies
efficiency globally.
For mechanisms where good performance requires that bidders do not bid above
their value, we identify the notion of a weakly smooth mechanism. Weakly smooth
mechanisms, such as the Vickrey auction, are approximately efficient under the
no-overbidding assumption. Similar to smooth mechanisms, weakly smooth
mechanisms behave well in composition, and have high quality outcome in
equilibrium (assuming no overbidding) both in the full information setting and
in the Bayesian setting, as well as in learning outcomes.
In most of the paper we assume participants have quasi-linear valuations. We
also extend some of our results to settings where participants have budget
constraints
A Unifying Hierarchy of Valuations with Complements and Substitutes
We introduce a new hierarchy over monotone set functions, that we refer to as
(Maximum over Positive Hypergraphs). Levels of the hierarchy
correspond to the degree of complementarity in a given function. The highest
level of the hierarchy, - (where is the total number of
items) captures all monotone functions. The lowest level, -,
captures all monotone submodular functions, and more generally, the class of
functions known as . Every monotone function that has a positive
hypergraph representation of rank (in the sense defined by Abraham,
Babaioff, Dughmi and Roughgarden [EC 2012]) is in -. Every
monotone function that has supermodular degree (in the sense defined by
Feige and Izsak [ITCS 2013]) is in -. In both cases, the
converse direction does not hold, even in an approximate sense. We present
additional results that demonstrate the expressiveness power of
-.
One can obtain good approximation ratios for some natural optimization
problems, provided that functions are required to lie in low levels of the
hierarchy. We present two such applications. One shows that the
maximum welfare problem can be approximated within a ratio of if all
players hold valuation functions in -. The other is an upper
bound of on the price of anarchy of simultaneous first price auctions.
Being in - can be shown to involve two requirements -- one
is monotonicity and the other is a certain requirement that we refer to as
(Positive Lower Envelope). Removing the monotonicity
requirement, one obtains the hierarchy over all non-negative
set functions (whether monotone or not), which can be fertile ground for
further research
Characterizing Optimal Adword Auctions
We present a number of models for the adword auctions used for pricing
advertising slots on search engines such as Google, Yahoo! etc. We begin with a
general problem formulation which allows the privately known valuation per
click to be a function of both the identity of the advertiser and the slot. We
present a compact characterization of the set of all deterministic incentive
compatible direct mechanisms for this model. This new characterization allows
us to conclude that there are incentive compatible mechanisms for this auction
with a multi-dimensional type-space that are {\em not} affine maximizers. Next,
we discuss two interesting special cases: slot independent valuation and slot
independent valuation up to a privately known slot and zero thereafter. For
both of these special cases, we characterize revenue maximizing and efficiency
maximizing mechanisms and show that these mechanisms can be computed with a
worst case computational complexity and respectively,
where is number of bidders and is number of slots. Next, we
characterize optimal rank based allocation rules and propose a new mechanism
that we call the customized rank based allocation. We report the results of a
numerical study that compare the revenue and efficiency of the proposed
mechanisms. The numerical results suggest that customized rank-based allocation
rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored
Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c)
Decision Sciences Seminar, Fuqua School of Business, Duke Universit
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
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
Smoothness for Simultaneous Composition of Mechanisms with Admission
We study social welfare of learning outcomes in mechanisms with admission. In
our repeated game there are bidders and mechanisms, and in each round
each mechanism is available for each bidder only with a certain probability.
Our scenario is an elementary case of simple mechanism design with incomplete
information, where availabilities are bidder types. It captures natural
applications in online markets with limited supply and can be used to model
access of unreliable channels in wireless networks.
If mechanisms satisfy a smoothness guarantee, existing results show that
learning outcomes recover a significant fraction of the optimal social welfare.
These approaches, however, have serious drawbacks in terms of plausibility and
computational complexity. Also, the guarantees apply only when availabilities
are stochastically independent among bidders.
In contrast, we propose an alternative approach where each bidder uses a
single no-regret learning algorithm and applies it in all rounds. This results
in what we call availability-oblivious coarse correlated equilibria. It
exponentially decreases the learning burden, simplifies implementation (e.g.,
as a method for channel access in wireless devices), and thereby addresses some
of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian
settings. Our main results are general composition theorems for smooth
mechanisms when valuation functions of bidders are lattice-submodular. They
rely on an interesting connection to the notion of correlation gap of
submodular functions over product lattices.Comment: Full version of WINE 2016 pape
Payment Rules through Discriminant-Based Classifiers
pdf: publications/dfjo_svmmd.pdf ps: publications/dfjo_svmmd.ps.gz tr: http://arxiv.org/abs/1208.1184 slides: publications/slides_svmmd.pdf http: http://dx.doi.org/10.1145/2559049 keywords: web,journal,selected,recent webnote: Earlier version appeared in the proc13thecold sort: 1401a cvnote: \contrib16%\selectedpdf: publications/dfjo_svmmd.pdf ps: publications/dfjo_svmmd.ps.gz tr: http://arxiv.org/abs/1208.1184 slides: publications/slides_svmmd.pdf http: http://dx.doi.org/10.1145/2559049 keywords: web,journal,selected,recent webnote: Earlier version appeared in the proc13thecold sort: 1401a cvnote: \contrib16%\selecte
Sequential Posted Price Mechanisms with Correlated Valuations
We study the revenue performance of sequential posted price mechanisms and
some natural extensions, for a general setting where the valuations of the
buyers are drawn from a correlated distribution. Sequential posted price
mechanisms are conceptually simple mechanisms that work by proposing a
take-it-or-leave-it offer to each buyer. We apply sequential posted price
mechanisms to single-parameter multi-unit settings in which each buyer demands
only one item and the mechanism can assign the service to at most k of the
buyers. For standard sequential posted price mechanisms, we prove that with the
valuation distribution having finite support, no sequential posted price
mechanism can extract a constant fraction of the optimal expected revenue, even
with unlimited supply. We extend this result to the the case of a continuous
valuation distribution when various standard assumptions hold simultaneously.
In fact, it turns out that the best fraction of the optimal revenue that is
extractable by a sequential posted price mechanism is proportional to ratio of
the highest and lowest possible valuation. We prove that for two simple
generalizations of these mechanisms, a better revenue performance can be
achieved: if the sequential posted price mechanism has for each buyer the
option of either proposing an offer or asking the buyer for its valuation, then
a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d
denotes the degree of dependence of the valuations, ranging from complete
independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we
generalize the sequential posted price mechanisms further, such that the
mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer
that depends on the valuations of all buyers except i's, we prove that a
constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be
extracted.Comment: 29 pages, To appear in WINE 201
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