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203
Truth revelation in approximately efficient combinatorial auctions
 Journal of the ACM
, 2002
"... Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard ..."
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Cited by 236 (1 self)
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Abstract. Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms—in particular, their truth revelation properties—assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.
Adwords and generalized online matching
 In FOCS ’05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competit ..."
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Cited by 146 (6 self)
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How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competitive ratios of 1 − 1/e for this problem. 1
Truthful and NearOptimal Mechanism Design via Linear Programming
"... We give a general technique to obtain approximation mechanisms that are truthful in expectation.We show that for packing domains, any ffapproximation algorithm that also bounds the integrality gapof the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanismthat is ..."
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Cited by 141 (12 self)
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We give a general technique to obtain approximation mechanisms that are truthful in expectation.We show that for packing domains, any ffapproximation algorithm that also bounds the integrality gapof the LP relaxation of the problem by ff can be used to construct an ffapproximation mechanismthat is truthful in expectation. This immediately yields a variety of new and significantly improved results for various problem domains and furthermore, yields truthful (in expectation) mechanisms withguarantees that match the best known approximation guarantees when truthfulness is not required. In particular, we obtain the first truthful mechanisms with approximation guarantees for a variety of multiparameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of O( p m) for combinatorial auctions (CAs), (1 + ffl) for multiunit CAs with B = \Omega (log m) copies ofeach item, and 2 for multiparameter knapsack problems (multiunit auctions). Our construction is based on considering an LP relaxation of the problem and using the classicVCG [25, 9, 12] mechanism to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by ff, where ff is the integrality gap of the problem, canbe represented as a convex combination of integer solutions, and by viewing this convex combination as specifying a probability distribution over integer solutions, we get a randomized, truthful in expectationmechanism. Our construction can be seen as a way of exploiting VCG in a computational tractable way even when the underlying socialwelfare maximization problem is NPhard.
The communication requirements of efficient allocations and supporting prices
 Journal of Economic Theory
, 2006
"... We show that any communication finding a Pareto efficient allocation in a privateinformation economy must also discover supporting Lindahl prices. In particular, efficient allocation of L indivisible objects requires naming a price for each of the 2 L ¡1 bundles. Furthermore, exponential communicat ..."
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Cited by 138 (18 self)
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We show that any communication finding a Pareto efficient allocation in a privateinformation economy must also discover supporting Lindahl prices. In particular, efficient allocation of L indivisible objects requires naming a price for each of the 2 L ¡1 bundles. Furthermore, exponential communication in L is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the valuations are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the objects are homogeneous, arbitrarily good approximation is obtained using exponentially less communication than that needed for exact efficiency.
Approximation algorithms for combinatorial auctions with complementfree bidders
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algori ..."
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Cited by 137 (27 self)
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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1
Nash Equilibria in Competitive Societies, with Applications to Facility Location, Traffic Routing and Auction
, 2002
"... We consider the following class of problems. The value of an outcome to a society is measured via a submodular utility function (submodularity has a natural economic interpretation: decreasing marginal utility). Decisions, however are controlled by noncooperative agents who seek to maximise their ..."
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Cited by 124 (6 self)
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We consider the following class of problems. The value of an outcome to a society is measured via a submodular utility function (submodularity has a natural economic interpretation: decreasing marginal utility). Decisions, however are controlled by noncooperative agents who seek to maximise their own private utility. We present, under some basic assumptions, guarantees on the social performance of Nash equilibria. For submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 2 of optimal, subject to a functiondependent additive term. For nondecreasing, submodular utility functions, any Nash equilibrium gives an expected social utility within a factor 1 + of optimal, where 0 1 is a number based upon the discrete curvature of the function. A condition under which all sets of social and private utility functions induce pure strategy Nash equilibria is presented. The case in which agents, themselves, make use of approximation algorithms in decision making is discussed and performance guarantees given. Finally we present some specific problems that fall into our framework. These include the competitive versions of the facility location problem and kmedian problem, a maximisation version of the traffic routing problem of Roughgarden and Tardos [16], and multipleitem auctions.
Optimal Approximation for the Submodular Welfare Problem in the value oracle model
 STOC'08
, 2008
"... In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this pap ..."
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Cited by 122 (11 self)
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In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S) : S ∈ I}, where f is monotone submodular and I is the collection of independent sets in some matroid. For both problems, a greedy algorithm is known to yield a 1/2approximation [21, 16]. In special cases where the matroid is uniform (I = {S: S  ≤ k}) [20] or the submodular function is of a special type [4, 2], a (1 − 1/e)approximation has been achieved and this is optimal for these problems in the value oracle model [22, 6, 15]. A (1 − 1/e)approximation for the general Submodular Welfare Problem has been known only in a stronger demand oracle model [4], where in fact 1 − 1/e can be improved [9]. In this paper, we develop a randomized continuous greedy algorithm which achieves a (1 − 1/e)approximation for the Submodular Welfare Problem in the value oracle model. We also show that the special case of n equal players is approximation resistant, in the sense that the optimal (1 − 1/e)approximation is achieved by a uniformly random solution. Using the pipage rounding technique [1, 2], we obtain a (1 − 1/e)approximation for submodular maximization subject to any matroid constraint. The continuous greedy algorithm has a potential of wider applicability, which we demonstrate on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.
Incentive compatible multi unit combinatorial auctions
 In TARK 03
, 2003
"... This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each g ..."
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Cited by 113 (13 self)
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This paper deals with multiunit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both online and offline scenarios. This is the first result where nonVCG mechanisms are derived for nonsingle minded bidders for a natural model of combinatorial auctions.
Achieving BudgetBalance with VickreyBased Payment Schemes in Exchanges
 In Proceedings of the 17th International Joint Conference on Artificial Intelligence
, 2001
"... Generalized Vickrey mechanisms have received wide attention in the literature because they are efficient and strategyproof, i.e. truthful bidding is optimal whatever the bids of other agents. However it is wellknown that it is impossible for an exchange, with multiple buyers and sellers, to be ..."
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Cited by 111 (20 self)
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Generalized Vickrey mechanisms have received wide attention in the literature because they are efficient and strategyproof, i.e. truthful bidding is optimal whatever the bids of other agents. However it is wellknown that it is impossible for an exchange, with multiple buyers and sellers, to be efficient and budgetbalanced, even putting strategyproofness to one side. A marketmaker in an efficient exchange must make more payments than it collects. We enforce budgetbalance as a hard constraint, and explore payment rules to distribute surplus after an exchange clears to minimize distance to Vickrey payments. Different rules lead to different levels of truthrevelation and efficiency. Experimental and theoretical analysis suggest a simple Threshold scheme, which gives surplus to agents with payments further than a certain threshold value from their Vickrey payments. The scheme appears able to exploit agent uncertainty about bids from other agents to reduce manipulation and boost allocative efficiency in comparison with other simple rules.
Truthful randomized mechanisms for combinatorial auctions
 IN STOC
, 2006
"... We design two computationallyefficient incentivecompatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentivecompatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion o ..."
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Cited by 108 (19 self)
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We design two computationallyefficient incentivecompatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentivecompatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an O(pm)approximation of the optimal social welfare for arbitrary bidder valuations  this is the best approximation possible in polynomial time. The second one obtains an O(log2 m) approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentivecompatible mechanism for this class which only provides an O(pm)approximation.