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67
Approximate Mechanism Design Without Money
, 2009
"... The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforc ..."
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Cited by 43 (15 self)
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The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
Inapproximability results for combinatorial auctions with submodular utility functions
 in Proceedings of WINE 2005
, 2005
"... We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodu ..."
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Cited by 36 (0 self)
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We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1 − 1/e � 0.632, unless P = NP. Our result is based on a reduction from a multiprover proof system for MAX3COLORING. 1
Incentive compatible regression learning
 IN THE ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2008
"... We initiate the study of incentives in a general machine learning framework. We focus on a gametheoretic regression learning setting where private information is elicited from multiple agents with different, possibly conflicting, views on how to label the points of an input space. This conflict pot ..."
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Cited by 30 (14 self)
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We initiate the study of incentives in a general machine learning framework. We focus on a gametheoretic regression learning setting where private information is elicited from multiple agents with different, possibly conflicting, views on how to label the points of an input space. This conflict potentially gives rise to untruthfulness on the part of the agents. In the restricted but important case when every agent cares about a single point, and under mild assumptions, we show that agents are motivated to tell the truth. In a more general setting, we study the power and limitations of mechanisms without payments. We finally establish that, in the general setting, the VCG mechanism goes a long way in guaranteeing truthfulness and economic efficiency.
Item Pricing for Revenue Maximization
"... We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected rev ..."
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Cited by 29 (4 self)
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We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of singleminded and unitdemand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2 O( √ log n log log n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2 Ω(log1/4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12, 10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers.
Setting lower bounds on truthfulness
 In Proceedings of the Eighteenth Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2007
"... We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several nonutilitarian multiparameter problems. In particular, we demonstrate the strength of our techniques by e ..."
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Cited by 26 (3 self)
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We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several nonutilitarian multiparameter problems. In particular, we demonstrate the strength of our techniques by exhibiting a lower bound of 2 − 1 m for the scheduling problem with unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic Mechanism Design). Our lower bound applies to truthful randomized mechanisms (disregarding any computational assumptions on the running time of these mechanisms). Moreover, it holds even for the weaker notion of truthfulness for randomized mechanisms – i.e., truthfulness in expectation. This lower bound nearly matches the known 7 4 (randomized) truthful upper bound for the case of two machines (a nontruthful FPTAS exists). No lower bound for truthful randomized mechanisms in multiparameter settings was previously known. We show an application of our techniques to the workloadminimization problem in networks. We prove our lower bounds for this problem in the interdomain routing setting presented by Feigenbaum, Papadimitriou, Sami, and Shenker. Finally, we discuss several notions of nonutilitarian “fairness ” (MaxMin fairness, MinMax fairness, and envy minimization). We show how our techniques can be used to prove lower bounds for these notions.
Limitations of VCGbased mechanisms
 In Proceedings of the 39th annual ACM symposium on Theory of computing
, 2007
"... We consider computationallyefficient incentivecompatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Specific ..."
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Cited by 18 (2 self)
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We consider computationallyefficient incentivecompatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an Ω(m 1 6) lower bound, which is close to the known upper bound of O(m 1 2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.
Singlevalue combinatorial auctions and algorithmic implementation in undominated strategies
 In ACM Symposium on Discrete Algorithms
, 2011
"... In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple ..."
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Cited by 18 (2 self)
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In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple the algorithmic allocation problem from the strategic aspects, by a procedure that converts any algorithm to a dominantstrategy ascending mechanism. This technique works for any single value domain, in which each agent has the same value for each desired outcome, and this value is the only private information. In particular, for “singlevalue CAs”, where each player desires any one of several different bundles but has the same value for each of them, our technique converts any approximation algorithm to a dominant strategy mechanism that almost preserves the original approximation ratio. Our second result provides the first computationally efficient deterministic mechanism for the case of singlevalue multiminded bidders (with private value and private desired bundles). The mechanism achieves an approximation to the social welfare which is close to the best possible in polynomial time (unless P=NP). This mechanism is an algorithmic implementation in undominated strategies, a notion that we define and justify, and is of independent interest. 1
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 18 (7 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. 1
Welfare Guarantees for Combinatorial Auctions with Item Bidding
, 2010
"... We analyze the price of anarchy (POA) in a simple and practical nontruthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate secondprice auctions. We first prove that under a standard “no overbidding ” ..."
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Cited by 17 (2 self)
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We analyze the price of anarchy (POA) in a simple and practical nontruthful combinatorial auction when players have subadditive valuations for goods. We study the mechanism that sells every good in parallel with separate secondprice auctions. We first prove that under a standard “no overbidding ” assumption, for every subadditive valuation profile, every pure Nash equilibrium has welfare at least 50 % of optimal — i.e., the POA is at most 2. For the incomplete information setting, we prove that the POA with respect to BayesNash equilibria is strictly larger than 2 — an unusual separation from the fullinformation model — and is at most 2 ln m, where m is the number of goods.
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 17 (4 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