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Mechanism Design via Machine Learning
 IN PROC. OF THE 46TH IEEE SYMP. ON FOUNDATIONS OF COMPUTER SCIENCE
, 2005
"... We use techniques from samplecomplexity in machine learning to reduce problems of incentivecompatible mechanism design to standard algorithmic questions, for a broad class of revenuemaximizing pricing problems. Our reductions imply that for these problems, given an optimal (or #approximation) al ..."
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Cited by 47 (11 self)
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We use techniques from samplecomplexity in machine learning to reduce problems of incentivecompatible mechanism design to standard algorithmic questions, for a broad class of revenuemaximizing pricing problems. Our reductions imply that for these problems, given an optimal (or #approximation) algorithm for the standard algorithmic problem, we can convert it into a (1 + #)approximation (or #(1 + #)approximation) for the incentivecompatible mechanism design problem, so long as the number of bidders is sufficiently large as a function of an appropriate measure of complexity of the comparison class of solutions. We apply these results to the problem of auctioning a digital good, to the attribute auction problem which includes a wide variety of discriminatory pricing problems, and to the problem of itempricing in unlimitedsupply combinatorial auctions. From a machine learning perspective, these settings present several challenges: in particular, the loss function is discontinuous and asymmetric, and the range of bidders' valuations may be large.
Item Pricing for Revenue Maximization
"... We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected rev ..."
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Cited by 29 (4 self)
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We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of singleminded and unitdemand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2 O( √ log n log log n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2 Ω(log1/4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12, 10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers.
Revenue monotonicity in combinatorial auctions
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2007
"... Intuitively, one might expect that a seller’s revenue from an auction weakly increases as the number of bidders grows, as this increases competition. However, it is known that for combinatorial auctions that use the VCG mechanism, a seller can sometimes increase revenue by dropping bidders. In this ..."
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Cited by 20 (3 self)
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Intuitively, one might expect that a seller’s revenue from an auction weakly increases as the number of bidders grows, as this increases competition. However, it is known that for combinatorial auctions that use the VCG mechanism, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this problem can occur under other dominantstrategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity ” are not limited to mechanisms that achieve efficient allocations. Instead, they can occur under any dominantstrategy direct mechanism that sets prices using critical values, and that always chooses an allocation that cannot be augmented to make some bidder better off, while making none worse off.
Automated online mechanism design and prophet inequalities
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2007
"... Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the ..."
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Cited by 17 (5 self)
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Recent work on online auctions for digital goods has explored the role of optimal stopping theory — particularly secretary problems — in the design of approximately optimal online mechanisms. This work generally assumes that the size of the market (number of bidders) is known a priori, but that the mechanism designer has no knowledge of the distribution of bid values. However, in many realworld applications (such as online ticket sales), the opposite is true: the seller has distributional knowledge of the bid values (e.g., via the history of past transactions in the market), but there is uncertainty about market size. Adopting the perspective of automated mechanism design, introduced by Conitzer and Sandholm, we develop algorithms that compute an optimal, or approximately optimal, online auction mechanism given access to this distributional knowledge. Our main results are twofold. First, we show that when the seller does not know the market size, no constantapproximation to the optimum efficiency or revenue is achievable in the worst case, even under the very strong assumption that bid values are i.i.d. samples from a distribution known to the seller. Second, we show that when the seller has distributional knowledge of the market size as well as the bid values, one can do well in several senses. Perhaps most interestingly, by combining dynamic programming with prophet inequalities (a technique from optimal stopping theory) we are able to design and analyze online mechanisms which are temporally strategyproof (even with respect to arrival and departure times) and approximately efficiency(revenue)maximizing. In exploring the interplay between automated mechanism design and prophet inequalities, we prove new prophet inequalities motivated by the auction setting.
A Theory of Expressiveness in Mechanisms
, 2007
"... A key trend in the world—especially in electronic commerce—is a demand for higher levels of expressiveness in the mechanisms that mediate interactions, such as the allocation of resources, matching of peers, and elicitation of opinions from large and diverse communities. Intuitively, one would think ..."
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Cited by 15 (9 self)
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A key trend in the world—especially in electronic commerce—is a demand for higher levels of expressiveness in the mechanisms that mediate interactions, such as the allocation of resources, matching of peers, and elicitation of opinions from large and diverse communities. Intuitively, one would think that this increase in expressiveness would lead to more efficient mechanisms (e.g., due to better matching of supply and demand). However, until now we have lacked a general way of characterizing the expressiveness of these mechanisms, analyzing how it impacts the actions taken by rational agents—and ultimately the outcome of the mechanism. In this technical report we introduce a general model of expressiveness for mechanisms. Our model is based on a new measure which we refer to as the maximum impact dimension. The measure captures the number of different ways that an agent can impact the outcome of a mechanism. We proceed to uncover a fundamental connection between this measure and the concept of shattering from computational learning theory. We also provide a way to determine an upper bound on the expected efficiency of any mechanism under its most efficient Nash equilibrium which, remarkably, depends only on the mechanism’s expressiveness. We show that for any setting and any prior over agent preferences, the
When analysis fails: Heuristic mechanism design via selfcorrecting procedures
 In Proc. 35th Conf. on Current Trends in Theory and Practice of Computer Science (SOFSEM’09
, 2009
"... Abstract. Computational mechanism design (CMD) seeks to understand how to design game forms that induce desirable outcomes in multiagent systems despite private information, selfinterest and limited computational resources. CMD finds application in many settings, in the public sector for wireless s ..."
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Cited by 10 (3 self)
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Abstract. Computational mechanism design (CMD) seeks to understand how to design game forms that induce desirable outcomes in multiagent systems despite private information, selfinterest and limited computational resources. CMD finds application in many settings, in the public sector for wireless spectrum and airport landing rights, to Internet advertising, to expressive sourcing in the supply chain, to allocating computational resources. In meeting the demands for CMD in these rich domains, we often need to bridge from the theory of economic mechanism design to the practice of deployable, computational mechanisms. A compelling example of this need arises in dynamic combinatorial environments, where classic analytic approaches fail and heuristic, computational approaches are required. In this talk I outline the direction of selfcorrecting mechanisms, which dynamically modify decisions via “output ironing ” to ensure truthfulness and provide a fully computational approach to mechanism design. For an application, I suggest heuristic mechanisms for dynamic auctions in which bids arrive over time and supply may also be uncertain. 1
Reducing Mechanism Design to Algorithm Design via Machine Learning
 IN THE PROCEEDINGS OF THE 46TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS) 2005, UNDER THE TITLE “MECHANISM DESIGN VIA MACHINE LEARNING
, 2007
"... We use techniques from samplecomplexity in machine learning to reduce problems of incentivecompatible mechanism design to standard algorithmic questions, for a broad class of revenuemaximizing pricing problems. Our reductions imply that for these problems, given an optimal (or βapproximation) al ..."
Abstract

Cited by 10 (3 self)
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We use techniques from samplecomplexity in machine learning to reduce problems of incentivecompatible mechanism design to standard algorithmic questions, for a broad class of revenuemaximizing pricing problems. Our reductions imply that for these problems, given an optimal (or βapproximation) algorithm for an algorithmic pricing problem, we can convert it into a (1 + ɛ)approximation (or β(1 + ɛ)approximation) for the incentivecompatible mechanism design problem, so long as the number of bidders is sufficiently large as a function of an appropriate measure of complexity of the class of allowable pricings. We apply these results to the problem of auctioning a digital good, to the attribute auction problem which includes a wide variety of discriminatory pricing problems, and to the problem of itempricing in unlimitedsupply combinatorial auctions. From a machine learning perspective, these settings present several challenges: in particular, the “loss function” is discontinuous, is asymmetric, and has a large range. We address these issues in part by introducing a new form of coveringnumber bound that is especially wellsuited to these problems and may be of independent interest.
Computationally feasible automated mechanism design: General approach and case studies
 In Proceedings of the 25th National Conference on Artificial Intelligence (AAAI10
, 2010
"... In many multiagent settings, a decision must be made based on the preferences of multiple agents, and agents may lie about their preferences if this is to their benefit. In mechanism design, the goal is to design procedures (mechanisms) for making the decision that work in spite of such strategic be ..."
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Cited by 10 (1 self)
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In many multiagent settings, a decision must be made based on the preferences of multiple agents, and agents may lie about their preferences if this is to their benefit. In mechanism design, the goal is to design procedures (mechanisms) for making the decision that work in spite of such strategic behavior, usually by making untruthful behavior suboptimal. In automated mechanism design, the idea is to computationally search through the space of feasible mechanisms, rather than to design them analytically by hand. Unfortunately, the most straightforward approach to automated mechanism design does not scale to large instances, because it requires searching over a very large space of possible functions. In this paper, we describe an approach to automated mechanism design that is computationally feasible. Instead of optimizing over all feasible mechanisms, we carefully choose a parameterized subfamily of mechanisms. Then we optimize over mechanisms within this family, and analyze whether and to what extent the resulting mechanism is suboptimal outside the subfamily. We demonstrate the usefulness of our approach with two case studies. Mechanism Design Preliminaries Mechanism design deals with making social decisions in systems involving multiple agents. For a given domain, let O be the set of all possible outcomes (social decisions). For example, in resource allocation problems, an outcome specifies who wins which resources, and, if monetary payments are allowed, how much each agent pays. We generally assume that the agents are rational in a gametheoretic sense, and that each agent’s preferences are private information for that agent. Let Θ be the space of all possible types that agents may have, where agent i’s type θi contains all i’s private information. We generally focus on directrevelation mechanisms, in which each agent makes a report ˆ θi ∈ Θ of her preferences to the mechanism, which then makes the
A New Approach To Auctions And Resilient Mechanism Design
 STOC’09: Proceedings of the 41st annual ACM symposium on Theory of computing
, 2009
"... We put forward a new approach to mechanism design, and exemplify it via a new mechanism guaranteeing significant revenue in unrestricted combinatorial auctions. Our mechanism • succeeds in a new and very adversarial collusion model; • works in a new, equilibriumless, and very strong solution concep ..."
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Cited by 8 (8 self)
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We put forward a new approach to mechanism design, and exemplify it via a new mechanism guaranteeing significant revenue in unrestricted combinatorial auctions. Our mechanism • succeeds in a new and very adversarial collusion model; • works in a new, equilibriumless, and very strong solution concept; • benchmarks its performance against the knowledge that the players have about each other; • is computationally efficient and preserves the players ’ privacy to an unusual extent. 1
Single price mechanisms for revenue maximization in unlimited supply combinatorial auctions
, 2007
"... In this note we generalize a result of Guruswami et. al [7], showing that in unlimitedsupply combinatorial auctions, a surprisingly simple mechanism that offers the same price for each item achieves revenue within a logarithmic factor of the total social welfare for bidders with general valuation f ..."
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Cited by 7 (3 self)
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In this note we generalize a result of Guruswami et. al [7], showing that in unlimitedsupply combinatorial auctions, a surprisingly simple mechanism that offers the same price for each item achieves revenue within a logarithmic factor of the total social welfare for bidders with general valuation functions (not just singleminded or unitdemand bidders as in [7]). We also extend this to the limitedsupply setting for the special case of bidders with additive valuations. These are both settings for which Likhodedov and Sandholm [9] provide logarithmic approximations but via much more complex bundlepricing mechanisms. 1