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31
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 35 (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
"... Abstract—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 mech ..."
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Cited by 25 (5 self)
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Abstract—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.
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 18 (4 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
Secondary spectrum auctions for symmetric and submodular bidders
 In Proc. 13th Conf. Electronic Commerce (EC
, 2012
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Truthful mechanisms with implicit payment computation
 In Proceedings of the 11th ACM conference on Electronic Commerce
, 2010
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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 11 (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.
Combinatorial Auctions with Restricted Complements
"... a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of complements is notoriously difficult, and this int ..."
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Cited by 11 (1 self)
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a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of complements is notoriously difficult, and this intractability has stymiedtheoretical progress in the area. For example, there are no known positive results for combinatorial auctionsinwhichbiddervaluationsaremultiparameterandnoncomplementfree,otherthantherelatively weak results known for general valuations. To make inroads on the problem of combinatorial auction design in the presence of complements, we propose a model for valuations with complements that is parameterized by the “size ” of the complements. The model permits a succinct representation, a variety of computationally efficient queries, and nontrivial welfaremaximizationalgorithmsandmechanisms.Specifically,ahypergraphr valuation v foragoodsetM is represented by a hypergraph H = (M,E), where every (hyper)edge e ∈ E contains at most r vertices and has a nonnegative weight we. Each good j ∈ M also has a nonnegative weight wj. The value v(S) for a subset S ⊆ M of goods is defined as the sum of the weights of the goods and edges entirely contained in S. We design the following polynomialtime approximation algorithms and truthful mechanismsfor welfare maximization with bidders with hypergraph valuations.
A Universallytruthful Approximation Scheme for Multiunit Auctions
, 2012
"... We present a randomized, polynomialtime approximation scheme for multiunit auctions. Our mechanism is truthful in the universal sense, i.e., a distribution over deterministically truthful mechanisms. Previously known approximation schemes were truthful in expectation which is a weaker notion of tr ..."
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Cited by 8 (0 self)
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We present a randomized, polynomialtime approximation scheme for multiunit auctions. Our mechanism is truthful in the universal sense, i.e., a distribution over deterministically truthful mechanisms. Previously known approximation schemes were truthful in expectation which is a weaker notion of truthfulness assuming risk neutral bidders. The existence of a universally truthful approximation scheme was questioned by previous work showing that multiunit auctions with certain technical restrictions on their output do not admit a polynomialtime, universally truthful mechanism with approximation factor better than two. Our new mechanism employs VCG payments in a nonstandard way: The deterministic mechanisms underlying our universally truthful approximation scheme are not maximal in range and do not belong to the class of affine maximizers which, on a first view, seems to contradict previous characterizations of VCGbased mechanisms. Instead, each of these deterministic mechanisms is composed of a collection of affine maximizers, one for each bidder. This yields a subjective variant of VCG in which payments for different bidders are defined on the basis of possibly different affine maximizers.
Beyond equilibria: Mechanisms for repeated combinatorial auctions
, 2009
"... We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of thei ..."
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Cited by 8 (5 self)
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We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply shortsighted bestresponse strategies. We ask: when can a blackbox approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm’s approximation factor on average over many iterations? We present a general reduction for a broad class of algorithms when agents minimize external regret. We also present a mechanism for the combinatorial auction problem that attains an O (√m) approximation on average when agents apply bestresponse dynamics.
Mechanisms for Risk Averse Agents, Without Loss
, 2012
"... Auctions in which agents ’ payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by co ..."
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Cited by 5 (0 self)
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Auctions in which agents ’ payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by computational complexity. For many of these mechanisms, which are often referred to as truthfulinexpectation, incentive compatibility is contingent on the assumption that agents are riskneutral. These mechanisms have been criticized on the grounds that this assumption is too strong, because “real ” agents are typically risk averse, and moreover their precise attitude towards risk is typically unknown apriori. In response, researchers in algorithmic mechanism design have sought the design of universallytruthful mechanisms — mechanisms for which incentivecompatibility makes no assumptions regarding agents ’ attitudes towards risk. Starting with the observation that universal truthfulness is strictly stronger than incentive compatibility in the presence of risk aversion, we show that any truthfulinexpectation mechanism can be generically transformed into a mechanism that is incentive compatible even when agents are risk averse, without modifying the mechanism’s allocation rule. The transformed mechanism does not require reporting of agents ’ risk profiles. Equivalently, our result can be stated as follows: Every (randomized) allocation rule that is implementable in dominant strategies when players are risk neutral is also implementable when players are endowed with an arbitrary and unknown concave utility function for money. Our result has two main implications: (1) A mechanism designer concerned with an objective which depends only on the allocation rule of the mechanism can feel free to design a truthfulinexpectation mechanism, knowing that the riskneutrality assumption can be removed by a generic blackbox transformation. (2) Studying universallytruthful mechanisms under the pretense of robustness to risk aversion is no longer justified. 1