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Truthful and NearOptimal Mechanism Design via Linear Programming
"... 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 gapof the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanismthat is ..."
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Cited by 134 (12 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 gapof the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanismthat 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 withguarantees 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 classicVCG [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, canbe 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 expectationmechanism. 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 mechanism design for multidimensional scheduling via cycle monotonicity
 In Proceedings 8th ACM Conference on Electronic Commerce (EC
, 2007
"... We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m) ..."
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Cited by 52 (12 self)
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We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m)approximation truthful mechanisms [22, 20]. We study a wellmotivated special case of this problem, where the processing time of a job on each machine may either be “low ” or “high”, and the low and high values are public and jobdependent. This preserves the multidimensionality of the domain, and generalizes the restrictedmachines (i.e., {pj, ∞}) setting in scheduling. We give a general technique to convert any capproximation algorithm to a 3capproximation truthfulinexpectation mechanism. This is one of the few known results that shows how to export approximation
Mechanism design for singlevalue domains
 In Proc. Nat. Conf. on Artificial Intelligence, AAAI05
, 2005
"... In “SingleValue domains”, each agent has the same private value for all desired outcomes. We formalize this notion and give new examples for such domains, including a “SAT domain ” and a “singlevalue combinatorial auctions ” domain. We study two informational models: where the set of desired out ..."
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Cited by 37 (5 self)
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In “SingleValue domains”, each agent has the same private value for all desired outcomes. We formalize this notion and give new examples for such domains, including a “SAT domain ” and a “singlevalue combinatorial auctions ” domain. We study two informational models: where the set of desired outcomes is public information (the “known ” case), and where it is private information (the “unknown ” case). Under the “known ” assumption, we present several truthful approximation mechanisms. Additionally, we suggest a general technique to convert any bitonic approximation algorithm for an unweighted domain (where agent values are either zero or one) to a truthful mechanism, with only a small approximation loss. In contrast, we show that even positive results from the “unknown single minded combinatorial auctions ” literature fail to extend to the “unknown ” singlevalue case. We give a characterization of truthfulness in this case, demonstrating that the difference is subtle and surprising.
Mechanisms for MultiUnit Auctions
 IN PROCEEDINGS OF THE ACM CONFERENCE ON ELECTRONIC COMMERCE (EC
, 2007
"... We present an incentivecompatible polynomialtime approximation scheme for multiunit auctions with general kminded player valuations. The mechanism fully optimizes over an appropriately chosen subrange of possible allocations and then uses VCG payments over this subrange. We show that obtaining ..."
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Cited by 37 (3 self)
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We present an incentivecompatible polynomialtime approximation scheme for multiunit auctions with general kminded player valuations. The mechanism fully optimizes over an appropriately chosen subrange of possible allocations and then uses VCG payments over this subrange. We show that obtaining a fully polynomialtime incentivecompatible approximation scheme, at least using VCG payments, is NPhard. For the case of valuations given by black boxes, we give a polynomialtime incentivecompatible 2approximation mechanism and show that no better is possible, at least using VCG payments.
An impossibility result for truthful combinatorial auctions with submodular valuations
 In ACM STOC
, 2011
"... ar ..."
On the power of randomization in algorithmic mechanism design
"... In many settings the power of truthful mechanisms is severely bounded. In this paper we use randomization to overcome this problem. In particular, we construct an FPTAS for multiunit auctions that is truthful in expectation, whereas there is evidence that no polynomialtime truthful deterministic m ..."
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Cited by 32 (8 self)
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In many settings the power of truthful mechanisms is severely bounded. In this paper we use randomization to overcome this problem. In particular, we construct an FPTAS for multiunit auctions that is truthful in expectation, whereas there is evidence that no polynomialtime truthful deterministic mechanism provides an approximation ratio better than 2. We also show for the first time that truthful in expectation polynomialtime mechanisms are provably stronger than polynomialtime universally truthful mechanisms. Specifically, we show that there is a setting in which: (1) there is a nonpolynomial time truthful mechanism that always outputs the optimal solution, and that (2) no universally truthful randomized mechanism can provide an approximation ratio better than 2 in polynomial time, but (3) an FPTAS that is truthful in expectation exists.
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 distr ..."
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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.
Truthful assignment without money
 In Proceedings of the 11th ACM Conference on Electronic Commerce (EC
, 2010
"... We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal ..."
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Cited by 25 (0 self)
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We study the design of truthful mechanisms that do not use payments for the generalized assignment problem (GAP) and its variants. An instance of the GAP consists of a bipartite graph with jobs on one side and machines on the other. Machines have capacities and edges have values and sizes; the goal is to construct a welfare maximizing feasible assignment. In our model of private valuations, motivated by impossibility results, the value and sizes on all jobmachine pairs are public information; however, whether an edge exists or not in the bipartite graph is a job’s private information. That is, the selfish agents in our model are the jobs, and their private information is their edge set. We want to design mechanisms that are truthful without money (henceforth strategyproof), and produce assignments whose welfare
BlackBox Randomized Reductions in Algorithmic Mechanism Design
"... We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mechanism th ..."
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Cited by 25 (5 self)
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We give the first blackbox reduction from arbitrary approximation algorithms to truthful approximation mechanisms for a nontrivial class of multiparameter problems. Specifically, we prove that every packing problem that admits an FPTAS also admits a truthfulinexpectation randomized mechanism that is an FPTAS. Our reduction makes novel use of smoothed analysis, by employing small perturbations as a tool in algorithmic mechanism design. We develop a “duality” between linear perturbations of the objective function of an optimization problem and of its feasible set, and use the “primal” and “dual” viewpoints to prove the running time bound and the truthfulness guarantee, respectively, for our mechanism.