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37
Approximate Mechanism Design Without Money
, 2009
"... The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforc ..."
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Cited by 58 (14 self)
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The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
Selling privacy at auction. In:
- Proceedings of the 12th ACM Conference on Electronic Commerce.
, 2011
"... ABSTRACT 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 ..."
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Cited by 51 (12 self)
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ABSTRACT 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 multi-unit 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 envy-free mechanisms, which correspond to the natural class of fixed-price 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.
Truthful Mechanisms for Agents that Value Privacy
, 2013
"... Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from the truthfulness; it is not incorporated in players â utility functions (and doing so has been shown to lead to non-truthfulness in some cases) ..."
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Cited by 26 (2 self)
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Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from the truthfulness; it is not incorporated in players â utility functions (and doing so has been shown to lead to non-truthfulness in some cases). In this work, we propose a new, general way of modelling privacy in players â utility functions. Specifically, we only assume that if an outcome o has the property that any report of player i would have led to o with approximately the same probability, then o has small privacy cost to player i. We give three mechanisms that are truthful with respect to our modelling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number n of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of n).
Take it or leave it: Running a survey when privacy comes at a cost
- In Internet and Network Economics
, 2012
"... In this paper, we consider the problem of estimating a potentially sensitive (individually stigmatizing) statistic on a population. In our model, individuals are concerned about their privacy, and experience some cost as a function of their privacy loss. Nevertheless, they would be willing to partic ..."
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Cited by 22 (12 self)
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In this paper, we consider the problem of estimating a potentially sensitive (individually stigmatizing) statistic on a population. In our model, individuals are concerned about their privacy, and experience some cost as a function of their privacy loss. Nevertheless, they would be willing to participate in the survey if they were compensated for their privacy cost. These cost functions are not publicly known, however, nor do we make Bayesian assumptions about their form or distribution. Individuals are rational and will misreport their costs for privacy if doing so is in their best interest. Ghosh and Roth recently showed in this setting, when costs for privacy loss may be correlated with private types, if individuals value differential privacy, no individually rational direct revelation mechanism can compute any non-trivial estimate of the population statistic. In this paper, we circumvent this impossibility result by proposing a modified notion of how individuals experience cost as a function of their privacy loss, and by giving a mechanism which does not operate by direct revelation. Instead, our mechanism has the ability to randomly approach individuals from a population and offer them a take-it-or-leave-it offer. This is intended to model the abilities of a surveyor who may stand on a street corner
Mechanism design in large games: Incentives and privacy. arXiv preprint arXiv:1207.4084,
, 2013
"... ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, ..."
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Cited by 20 (12 self)
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ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, rather it only has the power to suggestion outcomes on the basis of voluntary participation. We show that despite these restrictions, recommender mechanisms can implement equilibria of complete information games in settings of incomplete information under the condition that the game is large-i.e. that there are a large number of players, and any player's action affects any other's payoff by at most a small amount. Our result follows from a novel application of differential privacy. We show that any algorithm that computes a correlated equilibrium of a complete information game while satisfying a variant of differential privacy-which we call joint differential privacy-can be used as a recommender mechanism while satisfying our desired incentive properties. Our main technical result is an algorithm for computing a * We gratefully acknowledge the support of NSF Grant CCF-1101389. We thank Nabil Al-Najjar, Eduardo Azevdeo, Eric Budish, Tymofiy Mylovanov, Andy Postlewaite, Al Roth and Tim Roughgarden for helpful comments and discussions. correlated equilibrium of a large game while satisfying joint differential privacy. Although our recommender mechanisms are designed to satisfy game-theoretic properties, our solution ends up satisfying a strong privacy property as well. No group of players can learn "much" about the type of any player outside the group from the recommendations of the mechanism, even if these players collude in an arbitrary way. As such, our algorithm is able to implement equilibria of complete information games, without revealing information about the realized types.
The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal
, 2012
"... In this paper, we show that for any mechanism design problem, the exponential mechanism can be implemented as a truthful mechanism while still preserving differential privacy, if the objective is to maximize social welfare. Our instantiation of the exponential mechanism can be interpreted as a gener ..."
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Cited by 20 (2 self)
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In this paper, we show that for any mechanism design problem, the exponential mechanism can be implemented as a truthful mechanism while still preserving differential privacy, if the objective is to maximize social welfare. Our instantiation of the exponential mechanism can be interpreted as a generalization of the VCG mechanism in the sense that the VCG mechanism is the extreme case when the privacy parameter goes to infinity. To our knowledge, this is the first general tool for designing mechanisms that are both truthful and differentially private.
Is privacy compatible with truthfulness
- In Proceedings of the 4th conference on Innovations in Theoretical Computer Science. ACM
"... In the area of privacy-preserving data mining, a differentially private mechanism intuitively encourages people to share their data truthfully because they are at little risk of revealing their own information. However, we argue that this interpretation is incomplete because external incentives are ..."
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Cited by 17 (1 self)
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In the area of privacy-preserving data mining, a differentially private mechanism intuitively encourages people to share their data truthfully because they are at little risk of revealing their own information. However, we argue that this interpretation is incomplete because external incentives are necessary for people to participate in databases, and so data release mechanisms should not only be differentially private but also compatible with those incentives, otherwise the data collected may be false. We apply the notion of truthfulness from game theory. In certain settings, it turns out that existing differentially private mechanisms do not encourage participants to report their information truthfully. On the positive side, we exhibit a transformation that takes truthful mechanisms and transforms them into differentially private mechanisms that remain truthful. Our transformation applies to games where the type space is small and the goal is to optimize an insensitive quantity such as social welfare. Our transformation incurs only a small additive loss in optimality, and it is computationally efficient. Combined with the VCG mechanism, our transformation implies that there exists a differentially private, truthful, and approximately efficient mechanism for any social welfare game with small type space. We also study a model where an explicit numerical cost is assigned to the information leaked by a mechanism. We show that in this case, even differential privacy may not be strong enough of a notion to motivate people to participate truthfully. We show that mechanisms that release a perturbed histogram of the database may reveal too much information. We also show that, in general, any mechanism that outputs a synopsis that resembles the original database (such as the mechanism of Blum et al. (STOC ’08)) may reveal too much information. Of independent interest, one corollary of our techniques is a new lower bound on the sample complexity of differentially private non-interactive synopsis generators.
Asymptotically truthful equilibrium selection in large congestion games
- In Proceedings of the fifteenth ACM conference on Economics and computation
, 2014
"... Studying games in the complete information model makes them analytically tractable. How-ever, large n player interactions are more realistically modeled as games of incomplete informa-tion, where players may know little to nothing about the types of other players. Unfortunately, games in incomplete ..."
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Cited by 10 (8 self)
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Studying games in the complete information model makes them analytically tractable. How-ever, large n player interactions are more realistically modeled as games of incomplete informa-tion, where players may know little to nothing about the types of other players. Unfortunately, games in incomplete information settings lose many of the nice properties of complete infor-mation games: the quality of equilibria can become worse, the equilibria lose their ex-post properties, and coordinating on an equilibrium becomes even more difficult. Because of these problems, we would like to study games of incomplete information, but still implement equilibria of the complete information game induced by the (unknown) realized player types. This problem was recently studied by Kearns et al [17], and solved in large games by means of introducing a weak mediator: their mediator took as input reported types of players, and output suggested actions which formed a correlated equilibrium of the underlying game. Players had the option to play independently of the mediator, or ignore its suggestions, but crucially, if they decided to opt-in to the mediator, they did not have the power to lie about their type. In this paper, we rectify this deficiency in the setting of large congestion games. We give, in a sense, the weakest possible mediator: it cannot enforce participation, verify types, or enforce its suggestions. Moreover, our mediator implements a Nash equilibrium of the complete information game. We show that it is an (asymptotic) ex-post equilibrium of the incomplete information game for all players to use the mediator honestly, and that when they do so, they end up playing an approximate Nash equilibrium of the induced complete information game. In particular, truthful use of the mediator is a Bayes-Nash equilibrium in any Bayesian game for any prior.
Scheduling without payments
- In SAGT
, 2011
"... We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports value ˜ti j for a task instead of th ..."
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Cited by 8 (0 self)
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We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports value ˜ti j for a task instead of the actual one ti j, it will execute for time ˜ti j if it gets the task—unless the declared value ˜ti j is less than the actual value ti j, in which case, it will execute for time ti j. Our main technical result is an optimal mechanism for one task and n players which has approximation ratio (n + 1)/2. We also provide a matching lower bound, showing that no other truthful mechanism can achieve a better approximation ratio. This immediately gives an approximation ratio of (n + 1)/2 and n(n + 1)/2 for social cost and makespan minimization, respectively, for any number of tasks. 1
