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79
Frugal path mechanisms
, 2002
"... We consider the problem of selecting a low cost s − t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated VickreyClarkeGroves (VCG) mechanism, which pays a premium to induce the edg ..."
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Cited by 115 (2 self)
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We consider the problem of selecting a low cost s − t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated VickreyClarkeGroves (VCG) mechanism, which pays a premium to induce the edges to reveal their costs truthfully. We observe that this premium can be unacceptably high. There are simple instances where the mechanism pays Θ(k) times the actual cost of the path, even if there is an alternate path available that costs only (1 + ɛ) times as much. This inspires the frugal path problem, which is to design a mechanism that selects a path and induces truthful cost revelation without paying such a high premium. This paper contributes negative results on the frugal path problem. On two large classes of graphs, including ones having three nodedisjoint s − t paths, we prove that no reasonable mechanism can always avoid paying a high premium to induce truthtelling. In particular, we introduce a general class of min function mechanisms, and show that all min function mechanisms can be forced to overpay just as badly as VCG. On the other hand, we prove that (on two large classes of graphs) every truthful mechanism satisfying some reasonable properties is a min function mechanism. 1
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 103 (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
Approximation algorithms for combinatorial auctions with complementfree bidders
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algori ..."
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Cited by 94 (22 self)
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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1
Truthful and NearOptimal Mechanism Design via Linear Programming
, 2005
"... We give a general technique to obtain approximation mechanisms that are truthful in expectation.We show that for packing domains, any ffapproximation algorithm that also bounds the integrality gap of the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanism that ..."
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Cited by 87 (11 self)
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We give a general technique to obtain approximation mechanisms that are truthful in expectation.We show that for packing domains, any ffapproximation algorithm that also bounds the integrality gap of the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanism that is truthful in expectation. This immediately yields a variety of new and significantly improved results for various problem domains and furthermore, yields truthful (in expectation) mechanisms with guarantees that match the best known approximation guarantees when truthfulness is not required. In particular, we obtain the first truthful mechanisms with approximation guarantees for a variety of multiparameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of O( p m) for combinatorial auctions (CAs), (1 + ffl) for multiunit CAs with B = \Omega (log m) copies ofeach item, and 2 for multiparameter knapsack problems (multiunit auctions). Our construction is based on considering an LP relaxation of the problem and using the classic VCG [25, 9, 12] mechanism to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by ff, where ff is the integrality gap of the problem, can be represented as a convex combination of integer solutions, and by viewing this convex combination as specifying a probability distribution over integer solutions, we get a randomized, truthful in expectation mechanism. Our construction can be seen as a way of exploiting VCG in a computational tractable way even when the underlying socialwelfare maximization problem is NPhard.
Truthful randomized mechanisms for combinatorial auctions
 IN STOC
, 2006
"... We design two computationallyefficient incentivecompatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentivecompatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion o ..."
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Cited by 82 (15 self)
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We design two computationallyefficient incentivecompatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentivecompatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an O(pm)approximation of the optimal social welfare for arbitrary bidder valuations  this is the best approximation possible in polynomial time. The second one obtains an O(log2 m) approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentivecompatible mechanism for this class which only provides an O(pm)approximation.
Approximation techniques for utilitarian mechanism design
 IN PROC. 36TH ACM SYMP. ON THEORY OF COMPUTING
, 2005
"... This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonic ..."
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Cited by 64 (3 self)
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This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multiparameter agents. We focus on approximation algorithms for NPhard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques. Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for singleminded multiunit auctions. The best previous result for such auctions was a 2approximation. In addition,
Combination Can Be Hard: Approximability of the Unique Coverage Problem
 In Proceedings of the 17th Annual ACMSIAM Symposium on Discrete Algorithms
, 2006
"... Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we pro ..."
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Cited by 61 (3 self)
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Abstract We prove semilogarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we prove O(1 / logoe n) inapproximability for some constant oe = oe("). We also prove O(1 / log1/3 " n) inapproximability, forany "> 0, assuming that refuting random instances of 3SAT is hard on average; and prove O(1 / log n)inapproximability under a plausible hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish an \Omega (1 / log n)approximation algorithm, even for a moregeneral (budgeted) setting, and obtain an \Omega (1 / log B)approximation algorithm when every set hasat most B elements. We also show that our inapproximability results extend to envyfree pricing, animportant problem in computational economics. We describe how the (budgeted) unique coverage problem, motivated by realworld applications, has close connections to other theoretical problemsincluding max cut, maximum coverage, and radio broadcasting. 1 Introduction In this paper we consider the approximability of the following natural maximization analog of set cover: Unique Coverage Problem. Given a universe U = {e1,..., en} of elements, and given a collection S = {S1,..., Sm} of subsets of U. Find a subcollection S0 ` S to maximize the number of elements that are uniquely covered, i.e., appear in exactly one set of S 0.
Approximation Algorithms and Online Mechanisms for Item Pricing
 IN ACM CONFERENCE ON ELECTRONIC COMMERCE
, 2005
"... We present approximation and online algorithms for a number of problems of pricing items for sale so as to maximize 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 impr ..."
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Cited by 58 (9 self)
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We present approximation and online algorithms for a number of problems of pricing items for sale so as to maximize 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 recent independent work of Briest and Krysta [6] who achieve an O(k ) 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 w e on the edges, find prices p i 0 for the vertices to maximize (p i + p j ) .
CollusionResistant Mechanisms for SingleParameter Agents
 In Proceedings of the 16th Annual ACMSIAM Symposium on Discrete Algorithms
, 2005
"... We consider the problem of designing mechanisms with the incentive property that no coalition of agents can engage in a collusive strategy that results in an increase in the combined utility of the coalition. For single parameter agents, we give a characterization that essentially restricts such mec ..."
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Cited by 41 (7 self)
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We consider the problem of designing mechanisms with the incentive property that no coalition of agents can engage in a collusive strategy that results in an increase in the combined utility of the coalition. For single parameter agents, we give a characterization that essentially restricts such mechanisms to those that post a “take it or leave it ” price to for each agent in advance. We then consider relaxing the incentive property to only hold with high probability. In this relaxed model, we are able to design approximate profit maximizing auctions and approximately efficient auctions. We also give a general framework for designing mechanisms for single parameter agents while maintaining the coalition incentive property with high probability. In addition, we give several results for a weaker incentive property from the literature known as group strategyproofness.
On the Hardness of Being Truthful
 In 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS
, 2008
"... The central problem in computational mechanism design is the tension between incentive compatibility and computational ef ciency. We establish the rst significant approximability gap between algorithms that are both truthful and computationallyef cient, and algorithms that only achieve one of these ..."
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Cited by 40 (5 self)
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The central problem in computational mechanism design is the tension between incentive compatibility and computational ef ciency. We establish the rst significant approximability gap between algorithms that are both truthful and computationallyef cient, and algorithms that only achieve one of these two desiderata. This is shown in the context of a novel mechanism design problem which we call the COMBINATORIAL PUBLIC PROJECT PROBLEM (CPPP). CPPP is an abstraction of many common mechanism design situations, ranging from elections of kibbutz committees to network design. Our result is actually made up of two complementary results – one in the communicationcomplexity model and one in the computationalcomplexity model. Both these hardness results heavily rely on a combinatorial characterization of truthful algorithms for our problem. Our computationalcomplexity result is one of the rst impossibility results connecting mechanism design to complexity theory; its novel proof technique involves an application of the SauerShelah Lemma and may be of wider applicability, both within and without mechanism design. 1