Results 1  10
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38
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
Simple versus Optimal Mechanisms
"... The monopolist’s theory of optimal singleitem auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bid ..."
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Cited by 40 (14 self)
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The monopolist’s theory of optimal singleitem auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for singleitem auctions under the assumption that the agents ’ valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition. These fundamental guarantees for the Vickrey auction fail to hold in general singleparameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general singleparameter agent settings.
Selling Privacy at Auction
"... We initiate the study of markets for private data, through the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a ..."
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Cited by 22 (4 self)
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We initiate the study of markets for private data, through the lens of differential privacy. Although the purchase and sale of private data has already begun on a large scale, a theory of privacy as a commodity is missing. In this paper, we propose to build such a theory. Specifically, we consider a setting in which a data analyst wishes to buy information from a population from which he can estimate some statistic. The analyst wishes to obtain an accurate estimate cheaply, while the owners of the private data experience some cost for their loss of privacy, and must be compensated for this loss. Agents are selfish, and wish to maximize their profit, so our goal is to design truthful mechanisms. Our main result is that such problems can naturally be viewed and optimally solved as variants of multiunit procurement auctions. Based on this result, we derive auctions which are optimal up to small constant factors for two natural settings: 1. When the data analyst has a fixed accuracy goal, we show that an application of the classic Vickrey auction achieves the analyst’s accuracy goal while minimizing his total payment. 2. When the data analyst has a fixed budget, we give a mechanism which maximizes the accuracy of the resulting estimate while guaranteeing that the resulting sum payments do not exceed the analyst’s budget. In both cases, our comparison class is the set of envyfree mechanisms, which correspond to the natural class of fixedprice mechanisms in our setting. In both of these results, we ignore the privacy cost due to possible correlations between an individual’s private data and his valuation for privacy itself. We then show that generically, no individually rational mechanism can compensate individuals for the privacy loss incurred due to their reported valuations for privacy. This is nevertheless an important issue, and modeling it correctly is one of the many exciting directions for future work.
Sequential posted pricing and multiparameter mechanism design
 Proc. of 42 nd ACM STOC
"... We consider the classical mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize a given objective when allocating resources to selfinterested agents. In singleparameter settings (where each agent preference is given by a private value for being allo ..."
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Cited by 16 (4 self)
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We consider the classical mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize a given objective when allocating resources to selfinterested agents. In singleparameter settings (where each agent preference is given by a private value for being allocated the resource and zero for not being allocated) this problem is solved [19]. While this economic solution is tractable whenever the noneconomic optimization problem is tractable, it is complicated enough that it is rarely employed. Moreover, the techniques do not seem to generalize to multiparameter settings. Our first result is that for general product distributions on agent preferences and resource allocation problems that satisfy matroid properties (e.g., multiunit auctions, matchings, spanning trees), sequential posted price mechanisms, where agents are approached inturn and offered a precomputed takeitorleaveit offer, are at most a 4approximation to the optimal singleround mechanism. Furthermore, a suitable sequence of prices can be effectively computed by sampling the agents ’ distributional preferences. Notably, the analysis of this sequential posted price mechanism can be extended to give approximation mechanisms for the unsolved multiparameter setting. In stark contrast to the singleparameter setting, in multiparameter settings there is no general description or tractable implementation of optimal mechanisms. For decades, this unanswered issue has been widely considered one of the most important in the economic theory on mechanism design. We focus on
Efficiency and redistribution in dynamic mechanism design
 In EC 2008: ACM Conference on Electronic Commerce
, 2008
"... The emerging area of dynamic mechanism design seeks to achieve desirable equilibrium outcomes in multiagent sequential decisionmaking problems with selfinterest. Here we take the goal of maximizing social welfare. We start by extending the characterization result of Green & Laffont [1977] to a dy ..."
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Cited by 16 (4 self)
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The emerging area of dynamic mechanism design seeks to achieve desirable equilibrium outcomes in multiagent sequential decisionmaking problems with selfinterest. Here we take the goal of maximizing social welfare. We start by extending the characterization result of Green & Laffont [1977] to a dynamic setting, defining the dynamicGroves class of dynamic mechanisms and showing that it exactly corresponds to the set of mechanisms that are efficient (social welfare maximizing) and incentive compatible in an ex post equilibrium. The dynamicVCG mechanism of Bergemann & Välimäki [2006] is a dynamic analogue of the static VCG mechanism and is efficient, incentive compatible, and individual rational in an ex post equilibrium; we use our characterization result to show here that it is also revenue maximizing among all dynamic mechanisms with these properties. In other words, dynamicVCG maximizes the payments required of the agents and thus, while perhaps desirable for an auctioneer seeking high revenue, is in fact worst when maximizing agent utility is the goal. We then build on recent work on static redistribution mechanisms (see [Cavallo, 2006]) to design a dynamic redistribution mechanism for multiarmed bandit settings (e.g., the repeated allocation of a single good) that returns much of the revenue under dynamicVCG back to the agents, while maintaining the same efficiency, incentive compatibility, individual rationality, and nodeficit properties. We conclude with a numerical analysis, demonstrating empirically that this redistribution mechanism typically comes close to perfect budget balance.
Bayesian Incentive Compatibility via Fractional Assignments
"... Very recently, Hartline and Lucier [14] studied singleparameter mechanism design problems in the Bayesian setting. They proposed a blackbox reduction that converted Bayesian approximation algorithms into BayesianIncentiveCompatible (BIC) mechanisms while preserving social welfare. It remains a ma ..."
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Cited by 13 (3 self)
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Very recently, Hartline and Lucier [14] studied singleparameter mechanism design problems in the Bayesian setting. They proposed a blackbox reduction that converted Bayesian approximation algorithms into BayesianIncentiveCompatible (BIC) mechanisms while preserving social welfare. It remains a major open question if one can find similar reduction in the more important multiparameter setting. In this paper, we give positive answer to this question when the prior distribution has finite and small support. We propose a blackbox reduction for designing BIC multiparameter mechanisms. The reduction converts any algorithm into an ɛBIC mechanism with only marginal loss in social welfare. As a result, for combinatorial auctions with subadditive agents we get an ɛBIC mechanism that achieves constant approximation. 1
Limited and online supply and the Bayesian foundations of priorfree mechanism design
 In EC ’09
"... We study auctions for selling a limited supply of a single commodity in the case where the supply is known in advance and the case it is unknown and must be instead allocated in an online fashion. The latter variant was proposed by Mahdian and Saberi [12] as a model of an important phenomena in auct ..."
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Cited by 12 (4 self)
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We study auctions for selling a limited supply of a single commodity in the case where the supply is known in advance and the case it is unknown and must be instead allocated in an online fashion. The latter variant was proposed by Mahdian and Saberi [12] as a model of an important phenomena in auctions for selling Internet advertising: advertising impressions must be allocated as they arrive and the total quantity available is unknown in advance. We describe the Bayesian optimal mechanism for these variants and extend the random sampling auction of Goldberg et al. [8] to address the priorfree case.
Optimal Crowdsourcing Contests
"... We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as allpay auctions because entrants must exert effort upfront to enter. Unlike allpay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the ..."
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Cited by 12 (0 self)
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We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as allpay auctions because entrants must exert effort upfront to enter. Unlike allpay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2approximations to conventional methods for a large family of “regular ” distributions, and 4approximations, otherwise. 1
Incentive compatible budget elicitation in multiunit auctions
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2010
"... In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adapti ..."
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Cited by 8 (3 self)
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In this paper, we consider the problem of designing incentive compatible auctions for multiple (homogeneous) units of a good, when bidders have private valuations and private budget constraints. When only the valuations are private and the budgets are public, Dobzinski et al [8] show that the adaptive clinching auction is the unique incentivecompatible auction achieving Paretooptimality. They further show that this auction is not truthful with private budgets, so that there is no deterministic Paretooptimal auction with private budgets. Our main contribution is to show the following Budget Monotonicity property of this auction: When there is only one infinitely divisible good, a bidder cannot improve her utility by reporting a budget smaller than the truth. This implies that the adaptive clinching auction is incentive
Auctions with online supply
 In Fifth Workshop on Ad Auctions
, 2009
"... We study the problem of selling identical goods to n unitdemand bidders in a setting in which the total supply of goods is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider ..."
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Cited by 8 (2 self)
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We study the problem of selling identical goods to n unitdemand bidders in a setting in which the total supply of goods is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider two models of unknown supply: the adversarial supply model, in which the mechanism must produce a welfare guarantee for any arbitrary supply, and the stochastic supply model, in which supply is drawn from a distribution known to the mechanism, and the mechanism need only provide a welfare guarantee in expectation. Our main result is a separation between these two models. We show that all truthful mechanisms, even randomized, achieve a diminishing fraction of the optimal social welfare (namely, no better than a Ω(log log n) approximation) in the adversarial setting. In sharp contrast, in the stochastic model, under a standard monotone hazardrate condition, we present a truthful mechanism that achieves a constant approximation. We show that the monotone hazard rate condition is necessary, and also characterize a natural subclass of truthful mechanisms in our setting, the set of onlineenvyfree mechanisms. All of the mechanisms we present fall into this class, and we prove almost optimal lower bounds for such mechanisms. Since auctions with unknown supply are regularly run in many onlineadvertising settings, our main results emphasize the importance of considering distributional information in the design of auctions in such environments. 1