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194
Computationally feasible VCG mechanisms
 In Proceedings of the Second ACM Conference on Electronic Commerce (EC’00
, 2000
"... A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore comp ..."
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Cited by 188 (5 self)
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A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore computationally infeasible. However, if the optimal outcome is replaced by the results of a suboptimal algorithm, the resulting mechanism (termed VCGbased) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield nontruthful VCGbased mechanisms. We generalize these results for affine maximizers. The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCGbased mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm’s output. We provide a strong rationale for truthtelling behavior. Our method satisfies individual rationality as well.
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 182 (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.
Combinatorial auctions: A survey
, 2000
"... Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items ..."
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Cited by 170 (1 self)
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Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions. Second, it uses this subject as a vehicle to convey the aspects of integer programming that are relevant for the
Winner determination in combinatorial auction generalizations
, 2002
"... Combinatorial markets where bids can be submitted on bundles of items can be economically desirable coordination mechanisms in multiagent systems where the items exhibit complementarity and substitutability. There has been a surge of recent research on winner determination in combinatorial auctions. ..."
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Cited by 157 (23 self)
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Combinatorial markets where bids can be submitted on bundles of items can be economically desirable coordination mechanisms in multiagent systems where the items exhibit complementarity and substitutability. There has been a surge of recent research on winner determination in combinatorial auctions. In this paper we study a wider range of combinatorial market designs: auctions, reverse auctions, and exchanges, with one or multiple units of each item, with and without free disposal. We first theoretically characterize the complexity. The most interesting results are that reverse auctions with free disposal can be approximated, and in all of the cases without free disposal, even finding a feasible solution is ÆÈcomplete. We then ran experiments on known benchmarks as well as ones which we introduced, to study the complexity of the market variants in practice. Cases with free disposal tended to be easier than ones without. On many distributions, reverse auctions with free disposal were easier than auctions with free disposal— as the approximability would suggest—but interestingly, on one of the most realistic distributions they were harder. Singleunit exchanges were easy, but multiunit exchanges were extremely hard. 1
Combinatorial Auctions with Decreasing Marginal Utilities
, 2001
"... This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross s ..."
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Cited by 138 (21 self)
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This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zeromeasure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NPhard, we present an efficient greedy 2approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.
CABOB: A fast optimal algorithm for combinatorial auctions
"... Combinatorial auctions where bidders can bid on bundles of items can lead to more economical allocations, but determining the winners iscomplete and inapproximable. We present CABOB, a sophisticated search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also a ..."
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Cited by 122 (26 self)
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Combinatorial auctions where bidders can bid on bundles of items can lead to more economical allocations, but determining the winners iscomplete and inapproximable. We present CABOB, a sophisticated search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid ordering heuristics, and a host of structural observations. Experiments against CPLEX 7.0 show that CABOB is usually faster, never drastically slower, and in many cases drastically faster. We also uncover interesting aspects of the problem itself. First, the problems with short bids that were hard for the firstgeneration of specialized algorithms are easy. Second, almost all of the CATS distributions are easy, and become easier with more bids. Third, we test a number of random restart strategies, and show that they do not help on this problem because the runtime distribution does not have a heavy tail (at least not for CABOB). 1
Frugal path mechanisms
, 2002
"... We consider the problem of selecting a low cost s − t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated VickreyClarkeGroves (VCG) mechanism, which pays a premium to induce the edg ..."
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Cited by 115 (2 self)
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We consider the problem of selecting a low cost s − t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated VickreyClarkeGroves (VCG) mechanism, which pays a premium to induce the edges to reveal their costs truthfully. We observe that this premium can be unacceptably high. There are simple instances where the mechanism pays Θ(k) times the actual cost of the path, even if there is an alternate path available that costs only (1 + ɛ) times as much. This inspires the frugal path problem, which is to design a mechanism that selects a path and induces truthful cost revelation without paying such a high premium. This paper contributes negative results on the frugal path problem. On two large classes of graphs, including ones having three nodedisjoint s − t paths, we prove that no reasonable mechanism can always avoid paying a high premium to induce truthtelling. In particular, we introduce a general class of min function mechanisms, and show that all min function mechanisms can be forced to overpay just as badly as VCG. On the other hand, we prove that (on two large classes of graphs) every truthful mechanism satisfying some reasonable properties is a min function mechanism. 1
eMediator: A Next Generation Electronic Commerce Server
 Computational Intelligence
, 2002
"... This paper presents eMediator, an electronic commerce server prototype that demonstrates ways in which algorithmic support and gametheoretic incentive engineering can jointly improve the efficiency of ecommerce. eAuctionHouse, the configurable auction server, includes a variety of generalized combi ..."
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Cited by 106 (31 self)
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This paper presents eMediator, an electronic commerce server prototype that demonstrates ways in which algorithmic support and gametheoretic incentive engineering can jointly improve the efficiency of ecommerce. eAuctionHouse, the configurable auction server, includes a variety of generalized combinatorial auctions and exchanges, pricing schemes, bidding languages, mobile agents, and user support for choosing an auction type. We introduce two new logical bidding languages for combinatorial markets: the XOR bidding language and the ORofXORs bidding language. Unlike the traditional OR bidding language, these are fully expressive. They therefore enable the use of the ClarkeGroves pricing mechanism for motivating the bidders to bid truthfully. eAuctionHouse also supports supply/demand curve bidding. eCommitter, the leveled commitment contract optimizer, determines the optimal contract price and decommitting penalties for a variety of leveled commitment contracting mechanisms, taking into account that rational agents will decommit strategically in Nash equilibrium. It also determines the optimal decommitting strategies for any given leveled commitment contract. eExchangeHouse, the safe exchange planner, enables unenforced anonymous exchanges by dividing the exchange into chunks and sequencing those chunks to be delivered safely in alternation between the buyer and the seller.
Truthful approximation mechanisms for restricted combinatorial auctions
, 2002
"... When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We dev ..."
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Cited by 94 (3 self)
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When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCGlike payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O’Callaghan, and Shoham, who presented greedy heuristics. We show how to use IFTHENELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios. 1
Bidding languages for combinatorial auctions
 In Proc. 17th Intl. Joint Conference on Artif. Intell
, 2001
"... Combinatorial auctions provide a valuable mechanism for the allocation of goods in settings where buyer valuations exhibit complex structure with respect to substitutabilityand complementarity. Most algorithms are designed to work with explicit bids for concrete bundles of goods. However, logical bi ..."
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Cited by 91 (1 self)
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Combinatorial auctions provide a valuable mechanism for the allocation of goods in settings where buyer valuations exhibit complex structure with respect to substitutabilityand complementarity. Most algorithms are designed to work with explicit bids for concrete bundles of goods. However, logical bidding languages allow the expression of complex utility functions in a natural and concise way. We introduce a new, generalized language where bids are given by propositional formulae whose subformulae can be annotated with prices. This language allows bidder utilities to be formulated more naturally and concisely than existing languages. Furthermore, we outline a general algorithmic technique for winner determination for auctions that use this bidding language. 1