Results 1  10
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41
Truthful approximation schemes for singleparameter agents
 In FOCS ’08
"... We present the first monotone randomized polynomialtime approximation scheme (PTAS) for minimizing the makespan of parallel related machines (QCmax), the paradigmatic problem in singleparameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation ..."
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Cited by 42 (9 self)
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We present the first monotone randomized polynomialtime approximation scheme (PTAS) for minimizing the makespan of parallel related machines (QCmax), the paradigmatic problem in singleparameter algorithmic mechanism design. This result immediately gives a polynomialtime, truthful (in expectation) mechanism whose approximation guarantee attains the bestpossible one for all polynomialtime algorithms (assuming P ̸ = NP). Our algorithmic techniques are flexible and also yield a monotone deterministic quasiPTAS for QCmax and a monotone randomized PTAS for maxmin scheduling on related machines. 1
Bayesian combinatorial auctions: Expanding single buyer mechanisms to many buyers
 In FOCS. 512–521
"... • Bronze Medal, 13th International Olympiad in Informatics, Tampere, Finland, ..."
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Cited by 39 (2 self)
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• Bronze Medal, 13th International Olympiad in Informatics, Tampere, Finland,
Optimal multidimensional mechanism design: Reducing revenue to welfare maximization
, 2012
"... Bayesian auctions with arbitrary (possibly combinatorial) feasibility constraints and independent bidders with arbitrary (possibly combinatorial) demand constraints, appropriately extending Myerson’s singledimensional result [24] to this setting. We also show that every feasible Bayesian auction ca ..."
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Cited by 38 (13 self)
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Bayesian auctions with arbitrary (possibly combinatorial) feasibility constraints and independent bidders with arbitrary (possibly combinatorial) demand constraints, appropriately extending Myerson’s singledimensional result [24] to this setting. We also show that every feasible Bayesian auction can be implemented as a distribution over virtual VCG allocation rules. A virtual VCG allocation rule has the following simple form: Every bidder’s type ti is transformed into a virtual type fi(ti), via a bidderspecific function. Then, the allocation maximizing virtual welfare is chosen. Using this characterization, we show how to find and run the revenueoptimal auction given only black box access to an implementation of the VCG allocation rule. We generalize this result to arbitrarily correlated bidders, introducing the notion of a secondorder VCG allocation rule. We obtain our reduction from revenue to welfare optimization via two algorithmic results on reduced form auctions in settings with arbitrary feasibility and demand constraints. First, we provide a separation oracle for determining feasibility of a reduced form auction. Second, we provide a geometric algorithm to decompose any feasible reduced form into a distribution over virtual VCG allocation rules. In addition, we show how to execute both algorithms given only
From convex optimization to randomized mechanisms: Toward optimal combinatorial auctions
 In Proceedings of the 43rd annual ACM Symposium on Theory of Computing (STOC
, 2011
"... We design an expected polynomialtime, truthfulinexpectation, (1 − 1/e)approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass mostconcreteexamplesofsubmodular ..."
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Cited by 34 (11 self)
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We design an expected polynomialtime, truthfulinexpectation, (1 − 1/e)approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass mostconcreteexamplesofsubmodularfunctionsstudiedinthiscontext,includingcoveragefunctions, matroid weightedrank functions, and convex combinations thereof. Our approximation factor is the best possible, even for known and explicitly given coverage valuations, assuming P ̸ = NP. Ours is the first truthfulinexpectation and polynomialtime mechanism to achieve a constantfactor approximation for an NPhard welfare maximization problem in combinatorial auctions with heterogeneous goods and restricted valuations. Our mechanism is an instantiation of a new framework for designing approximation mechanisms based on randomized rounding algorithms. A typical such algorithm first optimizes over a fractional relaxation of the original problem, and then randomly rounds the fractional solution to an integral one. With rare exceptions, such algorithms cannot be converted into truthful mechanisms. The highlevel idea of our mechanism design framework is to optimize directly
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.
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 20 (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
Bayesian Incentive Compatibility via Matchings
"... We give a simple reduction from Bayesian incentive compatible mechanism design to algorithm design in settings where the agents ’ private types are multidimensional. The reduction preserves performance up to an additive loss that can be made arbitrarily small in polynomial time in the number of agen ..."
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Cited by 16 (1 self)
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We give a simple reduction from Bayesian incentive compatible mechanism design to algorithm design in settings where the agents ’ private types are multidimensional. The reduction preserves performance up to an additive loss that can be made arbitrarily small in polynomial time in the number of agents and the size of the agents ’ type spaces. 1
Reducing revenue to welfare maximization: Approximation algorithms and other generalizations
 IN SODA
, 2013
"... It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multidimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly comb ..."
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Cited by 13 (6 self)
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It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multidimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly combinatorial) demand constraints. This reduction provides a polytime solution to the optimal mechanism design problem in all auction settings where welfare optimization can be solved efficiently, but it is fragile to approximation and cannot provide solutions to settings where welfare maximization can only be tractably approximated. In this paper, we extend the reduction to accommodate approximation algorithms, providing an approximation preserving reduction from (truthful) revenue maximization to (not necessarily truthful) welfare maximization. The mechanisms output by our reduction choose allocations via blackbox calls to welfare approximation on randomly selected inputs, thereby generalizing also our earlier structural results on optimal multidimensional mechanisms to approximately optimal mechanisms. Unlike [12], our results here are obtained through novel uses of the Ellipsoid algorithm and other optimization techniques over nonconvex regions.
Understanding incentives: Mechanism design becomes algorithm design
, 2013
"... We provide a computationally efficient blackbox reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximationpreserving reduction from truthfully maximizing any objective under arbitrary feasibility constraints with arbitrary bidder types to ( ..."
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Cited by 10 (6 self)
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We provide a computationally efficient blackbox reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximationpreserving reduction from truthfully maximizing any objective under arbitrary feasibility constraints with arbitrary bidder types to (not necessarily truthfully) maximizing the same objective plus virtual welfare (under the same feasibility constraints). Our reduction is based on a fundamentally new approach: we describe a mechanism’s behavior indirectly only in terms of the expected value it awards bidders for certain behavior, and never directly access the allocation rule at all. Applying our new approach to revenue, we exhibit settings where our reduction holds both ways. That is, we also provide an approximationsensitive reduction from (nontruthfully) maximizing virtual welfare to (truthfully) maximizing revenue, and therefore the two problems are computationally equivalent. With this equivalence in hand, we show that both problems are NPhard to approximate within any polynomial factor, even for a single monotone submodular bidder. We further demonstrate the applicability of our reduction by providing a truthful mechanism maximizing fractional maxmin fairness. This is the first instance of a truthful mechanism that optimizes a nonlinear objective.
On the Limits of BlackBox Reductions in Mechanism Design
"... We consider the problem of converting an arbitrary approximation algorithm for a singleparameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are blackbox, meaning that they require only oracle access to the given algorithm and in particular ..."
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Cited by 8 (1 self)
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We consider the problem of converting an arbitrary approximation algorithm for a singleparameter optimization problem into a computationally efficient truthful mechanism. We ask for reductions that are blackbox, meaning that they require only oracle access to the given algorithm and in particular do not require explicit knowledge of the problem constraints. Such a reduction is known to be possible, for example, for the social welfare objective when the goal is to achieve Bayesian truthfulness and preserve social welfare in expectation. We show that a blackbox reduction for the social welfare objective is not possible if the resulting mechanism is required to be truthful in expectation and to preserve the worstcase approximation ratio of the algorithm to within a subpolynomial factor. Further, we prove that for other objectives such as makespan, no blackbox reduction is possible even if we only require Bayesian truthfulness and an averagecase performance guarantee.