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46
Mechanism design via differential privacy
 Proceedings of the 48th Annual Symposium on Foundations of Computer Science
, 2007
"... We study the role that privacypreserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differen ..."
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Cited by 106 (3 self)
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We study the role that privacypreserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differential privacy [15, 14], in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie. More precisely, mechanisms with differential privacy are approximate dominant strategy under arbitrary player utility functions, are automatically resilient to coalitions, and easily allow repeatability. We study several special cases of the unlimited supply auction problem, providing new results for digital goods auctions, attribute auctions, and auctions with arbitrary structural constraints on the prices. As an important prelude to developing a privacypreserving auction mechanism, we introduce and study a generalization of previous privacy work that accommodates the high sensitivity of the auction setting, where a single participant may dramatically alter the optimal fixed price, and a slight change in the offered price may take the revenue from optimal to zero. 1
Competitive Auctions
, 2002
"... We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of ..."
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Cited by 81 (10 self)
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We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of the profit of optimal fixed pricing for all inputs. We justify the use of optimal fixed pricing as a benchmark for evaluating competitive auction profit. We show that several randomized auctions are truthful and competitive and that no truthful deterministic auction is competitive. Our results extend to bounded supply markets, for which we also get truthful and competitive auctions.
Approximation Algorithms and Online Mechanisms for Item Pricing
, 2007
"... Abstract: We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller’s revenue in an unlimited supply setting. Our first result is an O(k)approximation algorithm for pricing items to singleminded bidders who each want at most ..."
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Cited by 60 (9 self)
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Abstract: We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller’s revenue in an unlimited supply setting. Our first result is an O(k)approximation algorithm for pricing items to singleminded bidders who each want at most k items. This improves over work of Briest and Krysta (2006) who achieve an O(k2) bound. For the case k = 2, where we obtain a 4approximation, this can be viewed as the following graph vertex pricing problem: given a (multi) graph G with valuations wi j on the edges, find prices pi ≥ 0 for the vertices to maximize {(i, j):wi j≥pi+p j} (pi + p j). We also improve the approximation of Guruswami et al. (2005) for the “highway problem” in which all desired subsets are intervals on a line, from O(logm+ logn) to O(logn), where m is the number of bidders and n is the number of items. Our approximation algorithms can
Knapsack Auctions
 Proceedings of the Seventeenth Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a pu ..."
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Cited by 58 (9 self)
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We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a publicly known size. For this setting, we consider the design of auctions in which agents have an incentive to truthfully reveal their private valuations. Following the framework of Goldberg et al. [10], we look to design an auction that obtains a constant fraction of the profit obtainable by a natural optimal pricing algorithm that knows the agents ’ valuations and object sizes. We give an auction that obtains a constant factor approximation in the nontrivial special case where the knapsack has unlimited capacity. We then reduce the limited capacity version of the problem to the unlimited capacity version via an approximately efficient auction (i.e., one that maximizes the social welfare). This reduction follows from generalizable principles. 1
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 46 (10 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.
Online Algorithms for Market Clearing
, 2002
"... In this paper we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to ..."
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Cited by 38 (4 self)
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In this paper we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to match without knowing what bids will arrive in the future. For maximizing profit, we present a (randomized) online algorithm with a competitive ratio of ln(p max min )+1, when bids are in a range [p min ,p max ], which we show is the best possible. A simpler algorithm has a ratio twice this, and can be used even if expiration times are not known. For maximizing the number of trades, we present a simple greedy algorithm that achieves a factor of 2 competitive ratio if no moneylosing trades are allowed. Interestingly, we show that if the online algorithm is allowed to subsidize matches  match moneylosing pairs if it has already collected enough money from previous pairs to pay for them  then it can be 1competitive with respect to the optimal offline algorithm that is not allowed subsidy. That is, the ability to subsidize is at least as valuable as knowing the future. We also consider the objectives of maximizing buy or sell volume, and present algorithms that achieve a competitive ratio of 2(ln(p max /p min ) + 1), or ln(p max /p min ) + 1 if the online algorithm is allowed subsidization. We show the latter is the best possible competitive ratio for this setting. For social welfare maximization we also obtain an optimal competitive ratio, which is below ln(p max /p min ). We present all of these results as corollaries of theorems on online matching in an incomplete interval graph.
Regret minimization under partial monitoring
 MATHEMATICS OF OPERATIONS RESEARCH
, 2004
"... We consider repeated games in which the player, instead of observing the action chosen by the opponent in each game round, receives a feedback generated by the combined choice of the two players. We study Hannan consistent players for this games; that is, randomized playing strategies whose perroun ..."
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Cited by 34 (7 self)
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We consider repeated games in which the player, instead of observing the action chosen by the opponent in each game round, receives a feedback generated by the combined choice of the two players. We study Hannan consistent players for this games; that is, randomized playing strategies whose perround regret vanishes with probability one as the number n of game rounds goes to infinity. We prove a general lower bound of Ω(n^−1/3) on the convergence rate of the regret, and exhibit a specific strategy that attains this rate on any game for which a Hannan consistent player exists.
Multiparameter mechanism design and sequential posted pricing
 CoRR
"... We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to selfinterested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent’s pr ..."
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Cited by 31 (4 self)
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We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to selfinterested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent’s preference is given by a single private value for being served and zero for not being served) this problem is solved [20]. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed [1], and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multidimensional setting (i.e., where each agent’s preference is given by multiple values for each of the multiple services available) [25]. In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered takeitorleaveit prices. We prove that these
Multiunit auctions with unknown supply
 ACM Conference on Electronic Commerce
, 2006
"... We study multiunit auctions for perishable goods, in a setting where the supply arrives online. This is motivated by its application in advertisement auctions on the internet. We give a 1competitive algorithm for computing the op4 timal single price auction assuming that all the agents report the ..."
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Cited by 23 (3 self)
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We study multiunit auctions for perishable goods, in a setting where the supply arrives online. This is motivated by its application in advertisement auctions on the internet. We give a 1competitive algorithm for computing the op4 timal single price auction assuming that all the agents report their bids truthfully. We use that algorithm to develop a truthful auction with a constant competitive ratio compared to the optimum offline singleprice auction. 1.
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.