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288
Improved algorithms for optimal winner determination in combinatorial auctions and generalizations
, 2000
"... Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NP-complete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper present ..."
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Cited by 582 (53 self)
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Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NP-complete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper presents a more sophisticated search algorithm for optimal (and anytime) winner determination, including structural improvements that reduce search tree size, faster data structures, and optimizations at search nodes based on driving toward, identifying and solving tractable special cases. We also uncover a more general tractable special case, and design algorithms for solving it as well as for solving known tractable special cases substantially faster. We generalize combinatorial auctions to multiple units of each item, to reserve prices on singletons as well as combinations, and to combinatorial exchanges -- all allowing for substitutability. Finally, we present algorithms for determining the winners in these generalizations.
Bidding and Allocation in Combinatorial Auctions
- IN ACM CONFERENCE ON ELECTRONIC COMMERCE
, 2000
"... When an auction of multiple items is performed, it is often desirable to allow bids on combinations of items, as opposed to only on single items. Such an auction is often called "combinatorial", and the exponential number of possible combinations results in computational intractability o ..."
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Cited by 275 (11 self)
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When an auction of multiple items is performed, it is often desirable to allow bids on combinations of items, as opposed to only on single items. Such an auction is often called "combinatorial", and the exponential number of possible combinations results in computational intractability of many aspects regarding such an auction. This paper considers two of these aspects: the bidding language and the allocation algorithm. First we consider which kinds of bids on combinations are allowed and how, i.e. in what language, they are specified. The basic tradeoff is the expressibility of the language versus its simplicity. We consider and formalize several bidding languages and compare their strengths. We prove exponential separations between the expressive power of different languages, and show that one language, "OR-bids with phantom items", can polynomially simulate the others. We then consider the problem of determining the best allocation -- a problem known to be computationally intractable. We suggest an approach based on Linear Programming (LP) and motivate it. We prove that the LP approach finds an optimal allocation if and only if prices can be attached to single items in the auction. We pinpoint several classes of auctions where this is the case, and suggest greedy and branch-and-bound heuristics based on LP for other cases.
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 230 (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.
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 216 (6 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 sub-optimal 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 non-truthful VCG-based 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 VCG-based 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 truth-telling behavior. Our method satisfies individual rationality as well.
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 215 (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
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 202 (25 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 zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation 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.
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 175 (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 ÆÈ-complete. 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. Single-unit exchanges were easy, but multi-unit exchanges were extremely hard. 1
Towards a universal test suite for combinatorial auction algorithms
- In ACM Electronic Commerce
, 2000
"... General combinatorial auctions—auctions in which bidders place unrestricted bids for bundles of goods—are the subject of increasing study. Much of this work has focused on algorithms for finding an optimal or approximately optimal set of winning bids. Comparatively little attention has been paid to ..."
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Cited by 162 (11 self)
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General combinatorial auctions—auctions in which bidders place unrestricted bids for bundles of goods—are the subject of increasing study. Much of this work has focused on algorithms for finding an optimal or approximately optimal set of winning bids. Comparatively little attention has been paid to methodical evaluation and comparison of these algorithms. In particular, there has not been a systematic discussion of appropriate data sets that can serve as universally accepted and well motivated benchmarks. In this paper we present a suite of distribution families for generating realistic, economically motivated combinatorial bids in five broad real-world domains. We hope that this work will yield many comments, criticisms and extensions, bringing the community closer to a universal combinatorial auction test suite.
Iterative Combinatorial Auctions: Achieving Economic and Computational Efficiency
- DEPARTMENT OF COMPUTER AND INFORMATION SCIENCE, UNIVERSITY OF PENNSYLVANIA
, 2001
"... This thesis presents new auction-based mechanisms to coordinate systems of selfinterested and autonomous agents, and new methods to design such mechanisms and prove their optimality... ..."
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Cited by 159 (19 self)
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This thesis presents new auction-based mechanisms to coordinate systems of selfinterested and autonomous agents, and new methods to design such mechanisms and prove their optimality...
