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63
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 Algorithmic Mechanism Design
, 2010
"... The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatib ..."
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Cited by 41 (11 self)
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The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatible mechanisms, namely that of Vickrey, Clarke, and Groves; and the central approach for circumventing computational obstacles, that of approximation algorithms, are fundamentally incompatible: natural applications of the VCG approach to an approximation algorithm fails to yield an incentive compatible mechanism. We consider relaxing the desideratum of (ex post) incentive compatibility (IC) to Bayesian incentive compatibility (BIC), where truthtelling is a BayesNash equilibrium (the standard notion of incentive compatibility in economics). For welfare maximization in singleparameter agent settings, we give a general blackbox reduction that turns any approximation algorithm into a Bayesian incentive compatible mechanism with essentially the same1 approximation factor.
The Price of Truthfulness for PayPerClick Auctions
, 2008
"... We analyze the problem of designing a truthful payperclick auction where the clickthroughrates (CTR) of the bidders are unknown to the auction. Such an auction faces the classic explore/exploit dilemma: while gathering information about the click through rates of advertisers, the mechanism may l ..."
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Cited by 36 (0 self)
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We analyze the problem of designing a truthful payperclick auction where the clickthroughrates (CTR) of the bidders are unknown to the auction. Such an auction faces the classic explore/exploit dilemma: while gathering information about the click through rates of advertisers, the mechanism may loose revenue; however, this gleaned information may prove valuable in the future for a more profitable allocation. In this sense, such mechanisms are prime candidates to be designed using multiarmed bandit techniques. However, a naive application of multiarmed bandit algorithms would not take into account the strategic considerations of the players — players might manipulate their bids (which determine the auction’s revenue) in a way as to maximize their own utility. Hence, we consider the natural restriction that the auction be truthful. The revenue that we could hope to achieve is the expected revenue of a Vickerey auction that knows the true CTRs, and we define the 2nd price regret to be the difference between the expected revenue of the auction and this Vickerey revenue. This work sharply characterizes what regret is achievable, under a truthful restriction. We show that this truthful restriction imposes statistical limits on the achievable regret — the achievable regret is Θ ∗ (T 2/3), while for traditional bandit algorithms (without the truthful restriction) the achievable regret is Θ ∗ (T 1/2) (where T is the number of rounds). We term the extra T 1/6 factor, the ‘price of truthfulness’.
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
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.
Price of Anarchy for Greedy Auctions
"... We study mechanisms for utilitarian combinatorial allocation problems, where agents are not assumed to be singleminded. This class of problems includes combinatorial auctions, multiunit auctions, unsplittable flow problems, and others. We focus on the problem of designing mechanisms that approximat ..."
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Cited by 30 (9 self)
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We study mechanisms for utilitarian combinatorial allocation problems, where agents are not assumed to be singleminded. This class of problems includes combinatorial auctions, multiunit auctions, unsplittable flow problems, and others. We focus on the problem of designing mechanisms that approximately optimize social welfare at every BayesNash equilibrium (BNE), which is the standard notion of equilibrium in settings of incomplete information. For a broad class of greedy approximation algorithms, we give a general blackbox reduction to deterministic mechanisms with almost no loss to the approximation ratio at any BNE. We also consider the special case of Nash equilibria in fullinformation games, where we obtain tightened results. This solution concept is closely related to the wellstudied price of anarchy. Furthermore, for a rich subclass of allocation problems, pure Nash equilibria are guaranteed to exist for our mechanisms. For many problems, the approximation factors we obtain at equilibrium improve upon the best known results for deterministic truthful mechanisms. In particular, we exhibit a simple deterministic mechanism for general combinatorial auctions that obtains an O(√m) approximation at every BNE.
Characterizing truthful multiarmed bandit mechanisms
 In ACMEC
, 2009
"... We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. I ..."
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Cited by 30 (1 self)
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We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer’s goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multiarmed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same“best”advertisement. We investigate how the design of multiarmed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties – essentially, they must separate exploration from exploitation – and they incur much higher regret than the optimal multiarmed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.
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.
The Exponential Mechanism for Social Welfare: Private, Truthful, and Nearly Optimal
, 2012
"... In this paper, we show that for any mechanism design problem, the exponential mechanism can be implemented as a truthful mechanism while still preserving differential privacy, if the objective is to maximize social welfare. Our instantiation of the exponential mechanism can be interpreted as a gener ..."
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Cited by 20 (2 self)
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In this paper, we show that for any mechanism design problem, the exponential mechanism can be implemented as a truthful mechanism while still preserving differential privacy, if the objective is to maximize social welfare. Our instantiation of the exponential mechanism can be interpreted as a generalization of the VCG mechanism in the sense that the VCG mechanism is the extreme case when the privacy parameter goes to infinity. To our knowledge, this is the first general tool for designing mechanisms that are both truthful and differentially private.