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Limitations of randomized mechanisms for combinatorial auctions
 In Proceedings of the 52nd IEEE Symposium on Foundations of Computer Science (FOCS
, 2011
"... Abstract — The design of computationally efficient and incentive compatible mechanisms that solve or approximate fundamental resource allocation problems is the main goal of algorithmic mechanism design. A central example in both theory and practice is welfaremaximization in combinatorial auctions. ..."
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Cited by 17 (3 self)
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Abstract — The design of computationally efficient and incentive compatible mechanisms that solve or approximate fundamental resource allocation problems is the main goal of algorithmic mechanism design. A central example in both theory and practice is welfaremaximization in combinatorial auctions. Recently, a randomized mechanism has been discovered for combinatorial auctions that is truthful in expectation and guarantees a (1 − 1/e)approximation to the optimal social welfare when players have coverage valuations [11]. This approximation ratio is the best possible even for nontruthful algorithms, assuming P ̸ = NP [16]. Given the recent sequence of negative results for combinatorial auctions under more restrictive notions of incentive compatibility [7], [2], [9], this development raises a natural question: Are truthfulinexpectation mechanisms compatible with polynomialtime approximation in a way that deterministic or universally truthful
Learning Valuation Functions
 25TH ANNUAL CONFERENCE ON LEARNING THEORY
, 2012
"... A core element of microeconomics and game theory is that consumers have valuation functions over bundles of goods and that these valuations functions drive their purchases. A common assumption is that these functions are subadditive meaning that the value given to a bundle is at most the sum of valu ..."
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A core element of microeconomics and game theory is that consumers have valuation functions over bundles of goods and that these valuations functions drive their purchases. A common assumption is that these functions are subadditive meaning that the value given to a bundle is at most the sum of values on the individual items. In this paper, we provide nearly tight guarantees on the efficient learnability of subadditive valuations. We also provide nearly tight bounds for the subclass of XOS (fractionally subadditive) valuations, also widely used in the literature. We additionally leverage the structure of valuations in a number of interesting subclasses and obtain algorithms with stronger learning guarantees.
The Computational Complexity of Truthfulness in Combinatorial Auctions
"... One of the fundamental questions of Algorithmic Mechanism Design is whether there exists an inherent clash between truthfulness and computational tractability: in particular, whether polynomialtime truthful mechanisms for combinatorial auctions are provably weaker in terms of approximation ratio th ..."
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Cited by 13 (1 self)
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One of the fundamental questions of Algorithmic Mechanism Design is whether there exists an inherent clash between truthfulness and computational tractability: in particular, whether polynomialtime truthful mechanisms for combinatorial auctions are provably weaker in terms of approximation ratio than nontruthful ones. This question was very recently answered for universally truthful mechanisms for combinatorial auctions [Dobzinski 2011], and even for truthfulinexpectation mechanisms [Dughmi and Vondrák 2011a]. However, both of these results are based on informationtheoretic arguments for valuations given by a value oracle, and leave open the possibility of polynomialtime truthful mechanisms for succinctly described classes of valuations. This paper is the first to prove computational hardness results for truthful mechanisms for combinatorial auctions with succinctly described valuations. We prove that there is a class of succinctly represented submodular valuations for which no deterministic truthful mechanism provides an m 1/2−ɛapproximation for a constant ɛ> 0, unless NP = RP (m denotes the number of items). Furthermore, we prove that even truthfulinexpectation mechanisms cannot approximate combinatorial auctions with certain succinctly described submodular valuations better than within n γ, where n is the number of bidders and γ> 0 some absolute constant, unless NP ⊆ P/poly. In addition, we prove computational hardness results for two related problems.
A Truthful Randomized Mechanism for Combinatorial Public Projects via Convex Optimization
, 2011
"... In Combinatorial Public Projects, there is a set of projects that may be undertaken, and a set of selfinterested players with a stake in the set of projects chosen. A public planner must choose a subset of these projects, subject to a resource constraint, with the goal of maximizing social welfare. ..."
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Cited by 10 (6 self)
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In Combinatorial Public Projects, there is a set of projects that may be undertaken, and a set of selfinterested players with a stake in the set of projects chosen. A public planner must choose a subset of these projects, subject to a resource constraint, with the goal of maximizing social welfare. Combinatorial Public Projects has emerged as one of the paradigmatic problems in Algorithmic Mechanism Design, a field concerned with solving fundamental resource allocation problems in the presence of both selfish behavior and the computational constraint of polynomialtime. We design a polynomialtime, truthfulinexpectation,(1−1/e)approximation mechanism for welfare maximization in a fundamental variant of combinatorial public projects. Our results apply to combinatorial public projects when players have valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions, matroid weightedrank functions, and convex combinations thereof. Our approximation factor is the best possible, assuming P ̸ = NP. Ours is the first mechanism that achieves a constant factor approximation for a natural NPhard variant of combinatorial public projects.
Communication Complexity of Combinatorial Auctions with Submodular Valuations
"... We prove the first communication complexity lower bound for constantfactor approximation of the submodular welfare problem. More precisely, we show that a (1 − 1 2e +ɛ)approximation ( ≃ 0.816) for welfare maximization in combinatorial auctions with submodular valuations would require exponential c ..."
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We prove the first communication complexity lower bound for constantfactor approximation of the submodular welfare problem. More precisely, we show that a (1 − 1 2e +ɛ)approximation ( ≃ 0.816) for welfare maximization in combinatorial auctions with submodular valuations would require exponential communication. We also show NPhardness of (1 − 1 2e +ɛ)approximation in a computational model where each valuation is given explicitly by a table of constant size. Both results rule out better than (1 − 1 2e)approximations in every oracle model with a separate oracle for each player, such as the demand oracle model. Our main tool is a new construction of monotone submodular functions that we call multipeak submodular functions. Roughly speaking, given a family of sets F, we construct a monotone submodular function f with a high value f(S) for every set S ∈ F (a “peak”), and a low value on every set that does not intersect significantly any set in F. We also study two other related problems: maxmin allocation (for which we also get hardness of
On the hardness of welfare maximization in combinatorial auctions with submodular valuations
, 2012
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On budgetbalanced groupstrategyproof cost sharing mechanisms
, 2012
"... A costsharing mechanism defines how to share the cost of a service among serviced customers. It solicits bids from potential customers and selects a subset of customers to serve and a price to charge each of them. The mechanism is groupstrategyproof if no subset of customers can gain by lying abou ..."
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A costsharing mechanism defines how to share the cost of a service among serviced customers. It solicits bids from potential customers and selects a subset of customers to serve and a price to charge each of them. The mechanism is groupstrategyproof if no subset of customers can gain by lying about their values. There is a rich literature that designs groupstrategyproof costsharing mechanisms using schemes that satisfy a property called crossmonotonicity. Unfortunately, Immorlica et al showed that for many services, crossmonotonic schemes are provably not budgetbalanced, i.e., they can recover only a fraction of the cost. While crossmonotonicity is a sufficient condition for designing groupstrategyproof mechanisms, it is not necessary. Pountourakis and Vidali recently provided a complete characterization of groupstrategyproof mechanisms. Using their characterization, we construct a fully budgetbalanced groupstrategyproof mechanism for the edgecover problem. This improves upon the crossmonotonic approach which can recover only half the cost, and provides a proofofconcept as to the usefullness of the complete characterization. This raises the question of whether all “natural ” problems have budgetbalanced groupstrategyproof mechanisms. We answer this question in the negative by