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73
Competitive Auctions
"... We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina co ..."
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Cited by 114 (12 self)
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We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibitseveral randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also givecompetitive auctions.
Knapsack auctions
"... 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 77 (12 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.
Auctions with Severely Bounded Communication
 In Proceedings of the 43rd Annual Symposium on Foundations of Computer Science (FOCS 02
, 2002
"... We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfaremaximizing and revenuemaximizing auctions under this communication restriction. For both measures, we determine the optimal auction an ..."
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Cited by 53 (8 self)
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We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfaremaximizing and revenuemaximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove nonsurprising properties of these kinds of auctions, e.g. that discrete prices are informationally ecient, as well as some surprising properties, e.g. that asymmetric auctions are better than symmetric ones.
Online Decision Problems with Large Strategy Sets
, 2005
"... In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the “strategy set”) whose costs vary over time. After T trials, the combined cost of the algorithm’s choices is compared with that of the single s ..."
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Cited by 34 (3 self)
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In an online decision problem, an algorithm performs a sequence of trials, each of which involves selecting one element from a fixed set of alternatives (the “strategy set”) whose costs vary over time. After T trials, the combined cost of the algorithm’s choices is compared with that of the single strategy whose combined cost is minimum. Their difference is called regret, and one seeks algorithms which are efficient in that their regret is sublinear in T and polynomial in the problem size. We study an important class of online decision problems called generalized multiarmed bandit problems. In the past such problems have found applications in areas as diverse as statistics, computer science, economic theory, and medical decisionmaking. Most existing algorithms were efficient only in the case of a small (i.e. polynomialsized) strategy set. We extend the theory by supplying nontrivial algorithms and lower bounds for cases in which the strategy set is much larger (exponential or infinite) and
Competitiveness via Consensus
, 2002
"... We introduce Consensus Revenue Estimate (CORE) auctions. This is a class of competitive auctions that is interesting for several reasons. One auction from this class achieves a better competitive ratio than any previously known auction. Another one uses only two random bits, whereas the previously k ..."
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Cited by 29 (9 self)
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We introduce Consensus Revenue Estimate (CORE) auctions. This is a class of competitive auctions that is interesting for several reasons. One auction from this class achieves a better competitive ratio than any previously known auction. Another one uses only two random bits, whereas the previously known competitive auctions on n bidders use n random bits. A parameterized CORE auction performs better than the previous auctions in the context of massmarket goods, such as digital goods. The improved performance is due to the consensus estimate technique that allows more information to be extracted from the input. This technique is very natural and may be useful in other contexts.
Revenue maximization with a single sample
 IN: PROCEEDINGS OF 12TH ACM CONFERENCE ON ELECTRONIC COMMERCE (2010
"... We design and analyze approximately revenuemaximizing auctions in general singleparameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation dis ..."
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Cited by 28 (6 self)
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We design and analyze approximately revenuemaximizing auctions in general singleparameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation distributions are a priori unknown to the seller. Despite this handicap, we show how to obtain approximately optimal expected revenue — nearly as large as what could be obtained if the distributions were known in advance — under quite general conditions. Our most general result concerns arbitrary downwardclosed singleparameter environments and valuation distributions that satisfy a standard hazard rate condition. We also assume that no bidder has a unique attribute value, which is obviously necessary with unknown and attributedependent valuation distributions. Here, we give an auction that, for every such environment and unknown valuation distributions, has expected revenue at least a constant fraction of the expected optimal welfare (and hence revenue). A key idea in our auction is to associate each bidder with another that has the same attribute, with the second bidder’s valuation acting as a random reserve price for the first. Conceptually, our analysis shows that even a single sample from a distribution — the second bidder’s valuation — is sufficient information to obtain nearoptimal expected revenue, even in quite general settings.
From Optimal Limited to Unlimited Supply Auctions
 In EC
, 2005
"... We investigate the class of singleround, sealedbid auctions for a set of identical items to bidders who each desire one unit. We adopt the worstcase competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal singleprice sale of least two items. In this p ..."
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Cited by 28 (7 self)
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We investigate the class of singleround, sealedbid auctions for a set of identical items to bidders who each desire one unit. We adopt the worstcase competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal singleprice sale of least two items. In this paper, we first derive an optimal auction for three items, answering an open question from [8]. Second, we show that the form of this auction is independent of the competitive framework used. Third, we propose a schema for converting a given limitedsupply auction into an unlimited supply auction. Applying this technique to our optimal auction for three items, we achieve an auction with a competitive ratio of 3.25, which improves upon the previously bestknown competitive ratio of 3.39 from [7]. Finally, we generalize a result from [8] and extend our understanding of the nature of the optimal competitive auction by showing that the optimal competitive auction occasionally offers prices that are higher than all bid values.
Market research and market design
 Advances in Theoretical Economics
, 2003
"... be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress. Advances in Theoretical Economics is one of The B.E. ..."
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Cited by 27 (0 self)
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be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, bepress. Advances in Theoretical Economics is one of The B.E.
On the Competitive Ratio of the Random Sampling Auction
 In Proc. 1st Workshop on Internet and Network Economics
, 2005
"... Abstract. We give a simple analysis of the competitive ratio of the random sampling auction from [10]. The random sampling auction was first shown to be worstcase competitive in [9] (with a bound of 7600 on its competitive ratio); our analysis improves the bound to 15. In support of the conjecture ..."
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Cited by 27 (7 self)
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Abstract. We give a simple analysis of the competitive ratio of the random sampling auction from [10]. The random sampling auction was first shown to be worstcase competitive in [9] (with a bound of 7600 on its competitive ratio); our analysis improves the bound to 15. In support of the conjecture that random sampling auction is in fact 4competitive, we show that on the equal revenue input, where any sale price gives the same revenue, random sampling is exactly a factor of four from optimal. 1 Introduction. Random sampling is the most prevalent technique for designing auctions to maximize the auctioneer’s profit when the bidders ’ valuations are a priori unknown [2–4, 7, 8, 10, 11]. The first and simplest application of random sampling to auctions is in the context of auctioning a digital good. 5 For this problem, the random
Foundations of Dominant Strategy Mechanisms
 REVIEW OF ECONOMIC STUDIES
, 2004
"... Wilson (1987) criticizes the existing literature of game theory as relying too much on commonknowledge assumptions. In reaction to Wilson’s critique, the recent literature of mechanism design has started employing simpler mechanisms such as dominant strategy mechanisms. However, there has been litt ..."
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Cited by 20 (0 self)
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Wilson (1987) criticizes the existing literature of game theory as relying too much on commonknowledge assumptions. In reaction to Wilson’s critique, the recent literature of mechanism design has started employing simpler mechanisms such as dominant strategy mechanisms. However, there has been little theory behind this approach. In particular, it has not been made clear why, when a mechanism designer is not willing to make strong commonknowledge assumptions, she would respond by using simpler mechanisms instead of even more complicated ones. This paper tries to fill the void and investigates some foundations for using simpler mechanisms such as dominant strategy mechanisms.