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40
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 79 (11 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.
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 56 (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
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 25 (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.
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 24 (2 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 21 (7 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.
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 20 (6 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
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 19 (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.
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 11 (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.
A Lower Bound on the Competitive Ratio of Truthful Auctions
 In Proceedings 21st Symposium on Theoretical Aspects of Computer Science
, 2004
"... Abstract We study a class of singleround, sealedbid auctions for a set of identical items. We adopt the worst case competitive framework defined by [1,2] that compares the profit of an auction to that of an optimal single price sale to at least two bidders. In this framework, we give a lower bound ..."
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Cited by 10 (4 self)
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Abstract We study a class of singleround, sealedbid auctions for a set of identical items. We adopt the worst case competitive framework defined by [1,2] that compares the profit of an auction to that of an optimal single price sale to at least two bidders. In this framework, we give a lower bound of 2.42 (an improvement from the bound of 2 given in [2]) on the competitive ratio of any truthful auction, one where each bidders best strategy is to declare the true maximum value an item is worth to them. This result contrasts with the 3.39 competitive ratio of the best known truthful auction [3]. 1
An Asymptotically Optimal Scheme for P2P File Sharing
 Harvard University
, 2004
"... The asymptotic analysis of certain public good models for p2p systems suggests that when the aim is to maximize social welfare a fixed contribution scheme in terms of the number of files shared can be asymptotically optimal as the number of participants n grows to infinity. Such a simple scheme elim ..."
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Cited by 8 (3 self)
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The asymptotic analysis of certain public good models for p2p systems suggests that when the aim is to maximize social welfare a fixed contribution scheme in terms of the number of files shared can be asymptotically optimal as the number of participants n grows to infinity. Such a simple scheme eliminates free riding, is incentive compatible and obtains a value of social welfare that is within o(n) of that obtained by the secondbest policy of the corresponding mechanism design formulation of the problem. We extend our model to account for file popularity, and discuss properties of the resulting equilibria. The fact that a simple optimization problem can be used to closely approximate the solution of the exact model (which is in most cases practically intractable both analytically and computationally), is of great importance for studying several interesting aspects of the system. We consider the evolution of the system to equilibrium in its early life, when both peers and the system planner are still learning about system parameters. We also analyse the case of group formation when peers belong to di#erent classes (such as DSL and dialup users), and it may be to their advantage to form distinct groups instead of a larger single group, or form such a larger group but avoid disclosing their class. We finally discuss the game that occurs when peers know that a fixed fee will be used, but the distribution of their valuations is unknown to the system designer.