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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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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
The Computational Complexity of Truthfulness in Combinatorial Auctions
 In Proceedings of the ACM Conference on Electronic Commerce (EC
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Simple and Nearly Optimal MultiItem Auctions
"... We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multiitem multibidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population. Second, every bidder’s value distributions of items are independen ..."
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We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian optimal multiitem multibidder auction problem under two conditions. First, bidders are independent, have additive valuations and are from the same population. Second, every bidder’s value distributions of items are independent but not necessarily identical monotone hazard rate (MHR) distributions. For noni.i.d. bidders, we also provide a PTAS when the number of bidders is small. Prior to our work, even for a single bidder, only constant factor approximations are known. Another appealing feature of our mechanism is the simple allocation rule. Indeed, the mechanism we use is either the secondprice auction with reserve price on every item individually, or VCG allocation with a few outlying items that requires additional treatments. It is surprising that such simple allocation rules suffice to obtain nearly optimal revenue. 1
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.
Understanding incentives: Mechanism design becomes algorithm design
 Proc. 54th IEEE Symp. on Foundations of Computer Science (FOCS
, 2013
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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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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.
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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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
Combinatorial Walrasian Equilibrium
"... We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing str ..."
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We study a combinatorial market design problem, where a collection of indivisible objects is to be priced and sold to potential buyers subject to equilibrium constraints. The classic solution concept for such problems is Walrasian Equilibrium (WE), which provides a simple and transparent pricing structure that achieves optimal social welfare. The main weakness of the WE notion is that it exists only in very restrictive cases. To overcome this limitation, we introduce the notion of a Combinatorial Walrasian equilibium (CWE), a natural relaxation of WE. The difference between a CWE and a (noncombinatorial) WE is that the seller can package the items into indivisible bundles prior to sale, and the market does not necessarily clear. We show that every valuation profile admits a CWE that obtains at least half of the optimal (unconstrained) social welfare. Moreover, we devise a polytime algorithm that, given an arbitrary allocation X, computes a CWE that achieves at least half of the welfare of X. Thus, the economic problem of finding a CWE with high social welfare reduces to the algorithmic problem of socialwelfare approximation. In addition, we show that every valuation profile admits a CWE that extracts a logarithmic fraction of the optimal welfare as revenue. Finally, these results are complemented by strong lower bounds when the seller is restricted to using item prices only, which motivates the use of bundles. The strength of our results derives partly from their generality — our results hold for arbitrary valuations that may exhibit complex combinations of substitutes and complements.
EfficiencyRevenue Tradeoffs in Auctions
"... Abstract. When agents with independent priors bid for a single item, Myerson’s optimal auction maximizes expected revenue, whereas Vickrey’s secondprice auction optimizes social welfare. We address the natural question of tradeoffs between the two criteria, that is, auctions that optimize, say, re ..."
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Abstract. When agents with independent priors bid for a single item, Myerson’s optimal auction maximizes expected revenue, whereas Vickrey’s secondprice auction optimizes social welfare. We address the natural question of tradeoffs between the two criteria, that is, auctions that optimize, say, revenue under the constraint that the welfare is above a given level. If one allows for randomized mechanisms, it is easy to see that there are polynomialtime mechanisms that achieve any point in the tradeoff (the Pareto curve) between revenue and welfare. We investigate whether one can achieve the same guarantees using deterministic mechanisms. We provide a negative answer to this question by showing that this is a (weakly) NPhard problem. On the positive side, we provide polynomialtime deterministic mechanisms that approximate with arbitrary precision any point of the tradeoff between these two fundamental objectives for the case of two bidders, even when the valuations are correlated arbitrarily. The major problem left open by our work is whether there is such an algorithm for three or more bidders with independent valuation distributions. 1