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53
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 ..."
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Cited by 278 (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, "ORbids 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 branchandbound heuristics based on LP for other cases. 1
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 181 (24 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
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 141 (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
Applying Learning Algorithms to Preference Elicitation in Combinatorial Auctions
, 2004
"... We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms ..."
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Cited by 59 (14 self)
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We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms perform a polynomial number of queries. We also give conditions under which the resulting algorithms have polynomial communication. Our conversion procedure allows us to generate combinatorial auction protocols from learning algorithms for polynomials, monotone DNF, and linearthreshold functions. In particular, we obtain an algorithm that elicits XOR bids with polynomial communication. We then characterize the communication requirements of implementing Vickrey payments with an elicitation algorithm. This suggests a modification to the queries in our elicitation algorithms so that truthful bidding becomes an expost Nash equilibrium.
Combinatorial auctions for supply chain formation
 in: Second ACM Conference on Electronic Commerce, 2000
"... Supply chain formation presents difficult coordination issues for distributed negotiation protocols. Agents must simultaneously negotiate production relationships at multiple levels, with important interdependencies among inputs and outputs at each level. Combinatorial auctions address this problem ..."
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Cited by 58 (2 self)
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Supply chain formation presents difficult coordination issues for distributed negotiation protocols. Agents must simultaneously negotiate production relationships at multiple levels, with important interdependencies among inputs and outputs at each level. Combinatorial auctions address this problem by global optimization over expressed offers to engage in compound exchanges. Optimizing with respect to offers results in optimal allocations if the offers reflect true values and costs. But autonomous selfinterested agents have an incentive to bid strategically in an attempt to gain
CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions
, 2005
"... Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NPcomplete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and ..."
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Cited by 58 (9 self)
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Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is NPcomplete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bidordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB’s search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the runtime distribution does not have a heavy tail.
Preference Elicitation and Query Learning
 Journal of Machine Learning Research
, 2004
"... In this paper we explore the relationship between "preference elicitation", a learningstyle problem that arises in combinatorial auctions, and the problem of learning via queries studied in computational learning theory. Preference elicitation is the process of asking questions about th ..."
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Cited by 42 (7 self)
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In this paper we explore the relationship between "preference elicitation", a learningstyle problem that arises in combinatorial auctions, and the problem of learning via queries studied in computational learning theory. Preference elicitation is the process of asking questions about the preferences of bidders so as to best divide some set of goods. As a learning problem, it can be thought of as a setting in which there are multiple target concepts that can each be queried separately, but where the goal is not so much to learn each concept as it is to produce an "optimal example". In this work, we prove a number of similarities and differences between twobidder preference elicitation and query learning, giving both separation results and proving some connections between these problems.
Solving Concisely Expressed Combinatorial Auction Problems
, 2002
"... Combinatorial auctions provide a valuable mechanism for the allocation of goods in settings where buyer valuations exhibit complex structure with respect to substitutability and complementarity. Most algorithms are designed to work with explicit "flat" bids for concrete bundles of goo ..."
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Cited by 40 (0 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 substitutability and complementarity. Most algorithms are designed to work with explicit "flat" bids for concrete bundles of goods. However, logical bidding languages allow the expression of complex utility functions in a natural and concise way, and have recently attracted considerable attention.
A MultiAgent Negotiation Testbed for Contracting Tasks with Temporal and Precedence Constraints
 INT’L JOURNAL OF ELECTRONIC COMMERCE
, 2002
"... We are interested in supporting multiagent contracting, in which customer agents solicit the resources and capabilities of other, selfinterested agents in order to accomplish their goals. Goals may ..."
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Cited by 37 (20 self)
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We are interested in supporting multiagent contracting, in which customer agents solicit the resources and capabilities of other, selfinterested agents in order to accomplish their goals. Goals may