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190
Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches
, 1999
"... In combinatorial auctions, multiple goods are sold simultaneously and bidders may bid for arbitrary combinations of goods. Determining the outcome of such an auction is an optimization problem that is NPcomplete in the general case. We propose two methods of overcoming this apparent intractability. ..."
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Cited by 288 (9 self)
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In combinatorial auctions, multiple goods are sold simultaneously and bidders may bid for arbitrary combinations of goods. Determining the outcome of such an auction is an optimization problem that is NPcomplete in the general case. We propose two methods of overcoming this apparent intractability. The first method, which is guaranteed to be optimal, reduces running time by structuring the search space so that a modified depthfirst search usually avoids even considering allocations that contain conflicting bids. Caching and pruning are also used to speed searching. Our second method is a heuristic, marketbased approach. It sets up a virtual multiround auction in which a virtual agent represents each original bid bundle and places bids, according to a fixed strategy, for each good in that bundle. We show through experiments on synthetic data that (a) our first method finds optimal allocations quickly and offers good anytime performance, and (b) in many cases our second method, despite lacking guarantees regarding optimality or running time, quickly reaches solutions that are nearly optimal. 1 Combinatorial Auctions Auction theory has received increasing attention from computer scientists in recent years. 1 One reason is the explosion of internetbased auctions. The use of auctions in businesstobusiness trades is also increasing rapidly [Cortese and Stepanek, 1998]. Within AI there is growing interest in using auction mechanisms to solve distributed resource allocation problems. For example, auctions and other market mechanisms are used in network bandwidth allocation, distributed configuration design, factory scheduling, and operating system memory allocation [Clearwater, 1996]. Marketoriented programming has
Privacy Preserving Auctions and Mechanism Design
, 1999
"... We suggest an architecture for executing protocols for auctions and, more generally, mechanism design. Our goal is to preserve the privacy of the inputs of the participants (so that no nonessential information about them is divulged, even a posteriori) while maintaining communication and computation ..."
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Cited by 238 (12 self)
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We suggest an architecture for executing protocols for auctions and, more generally, mechanism design. Our goal is to preserve the privacy of the inputs of the participants (so that no nonessential information about them is divulged, even a posteriori) while maintaining communication and computational efficiency. We achieve this goal by adding another party  the auction issuer  that generates the programs for computing the auctions but does not take an active part in the protocol. The auction issuer is not a trusted party, but is assumed not to collude with the auctioneer. In the case of auctions, barring collusion between the auctioneer and the auction issuer, neither party gains any information about the bids, even after the auction is over. Moreover, bidders can verify that the auction was performed correctly. The protocols do not require any communication between the bidders and the auction issuer and the computational efficiency is very reasonable. This architecture can be used to implement any mechanism design where the important factor is the complexity of the decision procedure.
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 224 (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 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 174 (22 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.
Flexible Double Auctions for Electronic Commerce: Theory and Implementation
, 1998
"... We consider a general family of auction mechanisms that admit multiple buyers and sellers, and determine marketclearing prices. We analyze the economic incentives facing participants in such auctions, demonstrating that, under some conditions, it is possible to induce truthful revelation of val ..."
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Cited by 149 (22 self)
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We consider a general family of auction mechanisms that admit multiple buyers and sellers, and determine marketclearing prices. We analyze the economic incentives facing participants in such auctions, demonstrating that, under some conditions, it is possible to induce truthful revelation of values by buyers or sellers, but not both, and for single but not multiunit bids. We also perform a computational analysis of the auctioneer's task, exhibiting efficient algorithms for processing bids and calculating allocations.
Competitive auctions and digital goods
 IN PROC. 12TH SYMP. ON DISCRETE ALG
, 2001
"... We study a class of single round, sealed bid auctions for items in unlimited supply such as digital goods. We focus on auctions that are truthful and competitive. Truthful auctions encourage bidders to bid their utility; competitive auctions yield revenue within a constant factor of the revenue fo ..."
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Cited by 134 (26 self)
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We study a class of single round, sealed bid auctions for items in unlimited supply such as digital goods. We focus on auctions that are truthful and competitive. Truthful auctions encourage bidders to bid their utility; competitive auctions yield revenue within a constant factor of the revenue for optimal fixed pricing. We show that for any truthful auction, even a multiprice auction, the expected revenue does not exceed that for optimal fixed pricing. We also give a bound on how far the revenue for optimal fixed pricing can be from the total market utility. We show that several randomized auctions are truthful and competitive under certain assumptions, and that no truthful deterministic auction is competitive. We present simulation results which confirm that our auctions compare favorably to fixed pricing. Some of our results extend to bounded supply markets, for which we also get truthful and competitive auctions.
Tycoon: An Implementation of a Distributed, Marketbased Resource Allocation System”, Multiagent Grid Systems
"... Distributed clusters like the Grid and PlanetLab enable the same statistical multiplexing efficiency gains for computing as the Internet provides for networking. One major challenge is allocating resources in an economically efficient and lowlatency way. A common solution is proportional share, whe ..."
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Cited by 111 (7 self)
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Distributed clusters like the Grid and PlanetLab enable the same statistical multiplexing efficiency gains for computing as the Internet provides for networking. One major challenge is allocating resources in an economically efficient and lowlatency way. A common solution is proportional share, where users each get resources in proportion to their predefined weight. However, this does not allow users to differentiate the value of their jobs. This leads to economic inefficiency. In contrast, systems that require reservations impose a high latency (typically minutes to hours) to acquire resources. We present Tycoon, a market based distributed resource allocation system based on proportional share. The key advantages of Tycoon are that it allows users to differentiate the value of their jobs, its resource acquisition latency is limited only by communication delays, and it imposes no manual bidding overhead on users. We present experimental results using a prototype implementation of our design. 1
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 109 (19 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.
Truth Revelation in Rapid, Approximately Efficient Combinatorial Auctions
 In ACM Conference on Electronic Commerce (EC99
, 1999
"... 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 co ..."
Abstract

Cited by 74 (5 self)
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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, which has empirically been shown to perform well. 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...