43 research outputs found
Expressiveness and Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of
the same problem, it is desirable to identify mechanisms that work well in a
wide range of circumstances. We pursue this goal for a position auction setting
and specifically seek mechanisms that guarantee good outcomes under both
complete and incomplete information. A variant of the generalized first-price
mechanism with multi-dimensional bids turns out to be the only standard
mechanism able to achieve this goal, even when types are one-dimensional. The
fact that expressiveness beyond the type space is both necessary and sufficient
for this kind of robustness provides an interesting counterpoint to previous
work on position auctions that has highlighted the benefits of simplicity. From
a technical perspective our results are interesting because they establish
equilibrium existence for a multi-dimensional bid space, where standard
techniques break down. The structure of the equilibrium bids moreover provides
an intuitive explanation for why first-price payments may be able to support
equilibria in a wider range of circumstances than second-price payments
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Expressiveness And Robustness of First-Price Position Auctions
Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments.Engineering and Applied Science
Efficiency Guarantees in Auctions with Budgets
In settings where players have a limited access to liquidity, represented in
the form of budget constraints, efficiency maximization has proven to be a
challenging goal. In particular, the social welfare cannot be approximated by a
better factor then the number of players. Therefore, the literature has mainly
resorted to Pareto-efficiency as a way to achieve efficiency in such settings.
While successful in some important scenarios, in many settings it is known that
either exactly one incentive-compatible auction that always outputs a
Pareto-efficient solution, or that no truthful mechanism can always guarantee a
Pareto-efficient outcome. Traditionally, impossibility results can be avoided
by considering approximations. However, Pareto-efficiency is a binary property
(is either satisfied or not), which does not allow for approximations.
In this paper we propose a new notion of efficiency, called \emph{liquid
welfare}. This is the maximum amount of revenue an omniscient seller would be
able to extract from a certain instance. We explain the intuition behind this
objective function and show that it can be 2-approximated by two different
auctions. Moreover, we show that no truthful algorithm can guarantee an
approximation factor better than 4/3 with respect to the liquid welfare, and
provide a truthful auction that attains this bound in a special case.
Importantly, the liquid welfare benchmark also overcomes impossibilities for
some settings. While it is impossible to design Pareto-efficient auctions for
multi-unit auctions where players have decreasing marginal values, we give a
deterministic -approximation for the liquid welfare in this setting
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
Моделі динаміки пружних збурень у неоднорідно деформованому континуумі
Розвинуто нелінійну теорію пружності стосовно задач томографії тензорних полів у неоднорідно деформованих твердих тілах. За визначальні параметри локального термодинамічного стану, що відповідають процесові деформування, прийнято тензорні характеристики, означені щодо актуальної (деформованої) конфігурації — тензор напружень Коші та міри деформації Альманзі або Фінґера. У рамках запропонованої нелінійної теорії побудовано декілька варіантів системи рівнянь динаміки малих пружних збурень у неоднорідно деформованому твердому континуумі, лінеаризованої стосовно деформації збурення. Коефіцієнти отриманих рівнянь залежать від локальних параметрів початкового напружено-деформованого стану, заданих в актуальній конфігурації. У такому вигляді їх зручно застосовувати для опису хвильових процесів, які збуджують у неоднорідно деформованих тілах, щоб отримати апостеріорну інформацію про актуальний напружено-деформований стан цих об’єктів.A nonlinear theory of elasticity as applied to problems of tensor fields tomography in non-uniformly strained solids has been developed. As constitutive thermodynamic parameters of the theory, corresponding the process of deformation, the tensor characteristics determinate in the actual configuration — tensors Almansi’s and Finger’s have been used. In the frame of the theory several variants of system equations for dynamics of small elastic disturbances in non-uniformly strained continuum, linearized with respect to the amplitude of the disturbance, have been built. These equations coefficients are depended on local parameters of the body stress-strained state, determined in local base of the actual configuration. In such a form they are convenient to use for describing of the wave processes in non-uniformly strained solids activated to obtain some a posteriori information about the actual stress-strained state of such objects.Развита нелинейная теория упругости применительно к задачам томографии тензорных полей в неоднородно деформированных твердых телах. В качестве определяющих параметров локального термодинамического состояния, соответствующих процессу деформирования, приняты тензорные характеристики, определяемые относительно актуальной (деформированной) конфигурации — тензор напряжений Коши и меры деформации Альманзи или Фингера. В рамках предложенной нелинейной теории построено несколько вариантов системы уравнений динамики малых упругих возмущений в неоднородно деформированном твердом континууме, линеаризированной относительно деформации возмущения. Коэффициенты полученных уравнений зависят от локальных параметров напряженно-деформированного состояния, заданных в актуальной конфигурации. В таком виде их удобно применять для описания волновых процессов, которые возбуждают в неоднородно деформированных телах для получения апостериорной информации об актуальном напряженно-деформированном состоянии этих объектов
Could the local population of the Lower Rhine delta supply the Roman army? Part 2: Modelling the carrying capacity using archaeological, palaeo-ecological and geomorphological data
Single-Sample Prophet Inequalities via Greedy-Ordered Selection
We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.</p
Unknown I.I.D. Prophets: Better Bounds, Streaming Algorithms, and a New Impossibility
A prophet inequality states, for some α ∈ [0, 1], that the expected value achievable by a gambler who
sequentially observes random variables X1, . . . , Xn and selects one of them is at least an α fraction
of the maximum value in the sequence. We obtain three distinct improvements for a setting that
was first studied by Correa et al. (EC, 2019) and is particularly relevant to modern applications in
algorithmic pricing. In this setting, the random variables are i.i.d. from an unknown distribution and
the gambler has access to an additional βn samples for some β ≥ 0. We first give improved lower
bounds on α for a wide range of values of β; specifically, α ≥ (1 + β)/e when β ≤ 1/(e − 1), which is
tight, and α ≥ 0.648 when β = 1, which improves on a bound of around 0.635 due to Correa et al.
(SODA, 2020). Adding to their practical appeal, specifically in the context of algorithmic pricing,
we then show that the new bounds can be obtained even in a streaming model of computation
and thus in situations where the use of relevant data is complicated by the sheer amount of data
available. We finally establish that the upper bound of 1/e for the case without samples is robust
to additional information about the distribution, and applies also to sequences of i.i.d. random
variables whose distribution is itself drawn, according to a known distribution, from a finite set of
known candidate distributions. This implies a tight prophet inequality for exchangeable sequences
of random variables, answering a question of Hill and Kertz (Contemporary Mathematics, 1992),
but leaves open the possibility of better guarantees when the number of candidate distributions is
small, a setting we believe is of strong interest to applications
Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game
We study the variant of the stable marriage problem in which the preferences
of the agents are allowed to include indifferences. We present a mechanism for
producing Pareto-stable matchings in stable marriage markets with indifferences
that is group strategyproof for one side of the market. Our key technique
involves modeling the stable marriage market as a generalized assignment game.
We also show that our mechanism can be implemented efficiently. These results
can be extended to the college admissions problem with indifferences
Prophet Inequalities for IID Random Variables from an Unknown Distribution
A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ ] ≥ α · E[maxt Xt ]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α ≥ 1 − 1/e ≈ 0.632, but quite recently a tight bound of α ≈ 0.745 was obtained. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α ≤ 1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1 − 1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n2) samples α ≥ 0.745 − ε for any ε > 0