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69
An efficient ascendingbid auction for multiple objects
 AMERICAN ECONOMIC REVIEW
, 1997
"... In multipleobject environments where individual bidders may demand more than one object, standard methods of auction generally result in allocative inefficiency. This paper proposes a new ascendingbid method for auctioning homogeneous goods, such as Treasury bills or communications spectrum. The a ..."
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Cited by 196 (26 self)
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In multipleobject environments where individual bidders may demand more than one object, standard methods of auction generally result in allocative inefficiency. This paper proposes a new ascendingbid method for auctioning homogeneous goods, such as Treasury bills or communications spectrum. The auctioneer announces a current price, bidders report back the quantity demanded at that price, and the auctioneer raises the price. Objects are awarded to bidders at the current price whenever they are “clinched,” and the process continues until the market clears. With pure private values, the proposed (dynamic) auction yields the same outcome as the (sealedbid) Vickrey auction, but may be simpler for bidders to understand and has the advantage of assuring the privacy of the upper portions of bidders ’ demand curves. With interdependent values, the proposed auction may still yield efficiency, whereas the Vickrey auction fails due to a problem which could be described as the “Generalized Winner’s Curse.”
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 142 (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.
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 115 (15 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.
The Lovely but Lonely Vickrey Auction
 Combinatorial Auctions, chapter 1
, 2006
"... William Vickrey’s (1961) inquiry into auctions and “counterspeculation ” marked the first serious attempt by an economist to analyze the details of market rules and to design new rules to achieve superior performance. He demonstrated that a particular pricing rule makes it a dominant strategy for bi ..."
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Cited by 55 (4 self)
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William Vickrey’s (1961) inquiry into auctions and “counterspeculation ” marked the first serious attempt by an economist to analyze the details of market rules and to design new rules to achieve superior performance. He demonstrated that a particular pricing rule makes it a dominant strategy for bidders to report their values truthfully, even when they
Linear Programming and Vickrey Auctions
, 2001
"... The Vickrey sealed bid auction occupies a central place in auction theory because of its efficiency and incentive properties. Implementing the auction requires the auctioneer to solve n + 1 optimization problems,where n is the number of bidders. In this paper we survey various environments (some old ..."
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Cited by 49 (0 self)
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The Vickrey sealed bid auction occupies a central place in auction theory because of its efficiency and incentive properties. Implementing the auction requires the auctioneer to solve n + 1 optimization problems,where n is the number of bidders. In this paper we survey various environments (some old and some new) where the payments bidders make under the Vickrey auction correspond to dual variables in certain linear programs. Thus,in these environments,at most two optimization problems must be solved to determine the Vickrey outcome. Furthermore,primaldual algorithms for some of these linear programs suggest ascending auctions that implement the Vickrey outcome.
The clockproxy auction: A practical combinatorial auction design
, 2006
"... We propose the clockproxy auction as a practical means for auctioning many related items. A clock auction phase is followed by a lastandfinal proxy round. The approach combines the simple and transparent price discovery of the clock auction with the efficiency of the proxy auction. Linear pricing ..."
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Cited by 48 (6 self)
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We propose the clockproxy auction as a practical means for auctioning many related items. A clock auction phase is followed by a lastandfinal proxy round. The approach combines the simple and transparent price discovery of the clock auction with the efficiency of the proxy auction. Linear pricing is maintained as long as possible, but then is abandoned in the proxy round to improve efficiency and enhance seller revenues. The approach has many advantages over the simultaneous ascending auction. In particular, the clockproxy auction has no exposure problem, eliminates incentives for demand reduction, and prevents most collusive bidding strategies. 1
Bundling Equilibrium in Combinatorial Auctions
, 2001
"... This paper analyzes individuallyrational ex post equilibrium in the VC (VickreyClarke) combinatorial auctions. If \Sigma is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in \Sigma. The \SigmaVC combinatorial aucti ..."
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Cited by 45 (8 self)
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This paper analyzes individuallyrational ex post equilibrium in the VC (VickreyClarke) combinatorial auctions. If \Sigma is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in \Sigma. The \SigmaVC combinatorial auctions (multigood auctions) obtained in this way are known to be individuallyrational truthtelling mechanisms. In contrast, this paper deals with nonrestricted VC auctions, in which the buyers restrict themselves to bids on bundles in \Sigma, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in \Sigma, they are in an equilibrium. We fully characterize those \Sigma that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in \Sigma represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partitionbased equilibrium, in which \Sigma is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partitionbased equilibrium.
On Ascending Vickrey Auctions for Heterogeneous Objects
, 2005
"... We construct an ascending auction for heterogeneous objects by applying a primaldual algorithm to a linear program that represents the efficientallocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. ..."
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Cited by 44 (4 self)
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We construct an ascending auction for heterogeneous objects by applying a primaldual algorithm to a linear program that represents the efficientallocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder’s prices are increased when he belongs to a “minimally undersupplied ” set of bidders. This concept generalizes the notion of “overdemanded” sets of objects introduced by Demange et al. (1986) for the onetoone assignment problem. Under a submodularity condition, the auction implements the Vickrey–Clarke–Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascendingauction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to various ascending auctions in the literature.
Multiunit auctions with budget limits
 In Proc. of the 49th Annual Symposium on Foundations of Computer Science (FOCS
, 2008
"... We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal ..."
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Cited by 35 (5 self)
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We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal allocation. We also obtain some surprising positive results for certain special cases. 1