There is interest in designing simultaneous auctions for situations in which the value of assets to a bidder depends upon which other assets he or she wins. In such cases, bidders may well wish to submit bids for combinations of assets. When this is allowed, the problem of determining the revenue maximizing set of nonconflicting bids can be a difficult one. We analyze this problem, identifying several different structures of combinatorial bids for which computational tractability is constructively demonstrated and some structures for which computational tractability 1 Introduction Some auctions sell many assets simultaneously. Often these assets, like U.S. treasury bills, are interchangeable. However, sometimes the assets and the bids for them are distinct. This happens frequently, as in the U.S. Department of the Interior's simultaneous sales of off-shore oil leases, in some private farm land auctions, and in the Federal Communications Commission's recent multi-billion dollar sales...

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 NP-complete 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 depth-first 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, market-based approach. It sets up a virtual multi-round 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 internet-based auctions. The use of auctions in business-to-business 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]. Market-oriented programming has

Auctions have emerged as the primary means of assigning spectrum licenses to companies wishing to provide wireless communication services. Since July 1994, the Federal Communications Commission (FCC) has conducted 33 spectrum auctions, assigning thousands of licenses to hundreds of firms. Countries throughout the world are conducting similar auctions. I review the current state of spectrum auctions. Both the design and performance of these auctions are addressed.

One of the major achievements of mechanism design theory is the family of truthful (incentive compatible) mechanisms often called VCG (named after Vickrey, Clarke and Groves). When applying VCG mechanisms to complex mechanism design problems such as combinatorial auctions a problem emerges: even finding optimal outcomes is computationally intractable. A striking observation is that if the optimal outcome is replaced by the results of computationally tractable approximation algorithms or heuristics then the resulting mechanism (termed VCG-based) is no longer necessarily truthful! The first part of this paper considers this problem in depth and shows that it is almost 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. The second part of this paper proposes a method for handling this non-truthfulness. We introduce a...

I review the uses of economic theory in the initial design and later improvement of the ‘‘simultaneous ascending auction,’ ’ which was developed initially for the sale of radio spectrum licenses in the United States. I analyze some capabilities and limitations of the auction, the roles of various detailed rules, the possibilities for introducing combinatorial bidding, and some considerations in adapting the auction for sales in which revenue, rather than efficiency, is the primary goal. I.

Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auction-based solutions to resource allocation problems with agents that have non-additive values for resources, such as distributed scheduling and task assignment problems. We introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic best-response bidding. Its optimality is proved with a novel connection to primal-dual optimization theory. We demonstrate orders of magnitude performance improvements over the only other known optimal combinatorial auction, the Generalized Vickrey Auction.

The US government recently sold spectrum rights using an innovative auction design, the simultaneous ascending auction, invented by economic theorists. The auction outcomes were broadly consistent with the expectations of the theorists. The auction form should have many other applications. March 21, 1998 Just as the Nobel committee was recognizing game theory's role in economics by awarding the 1994 prize to John Nash, John Harsanyi, and Reinhard Selten, game theory was being put to its biggest use ever. Billions of dollars worth of spectrum licenses were being sold by the US government, using a novel auction form designed by economic theorists. Suddenly, game theory became news. William Safire in the New York Times called it "the greatest auction in history." The Economist remarked, "When government auctioneers need worldly advice, where can they turn? To mathematical economists, of course . . . As for the firms that want to get their hands on a sliver of the airwaves, their best bet is to go out first and hire themselves a good game theorist." Fortune said it was the "most dramatic example of game theory's new power . . . It was a triumph, not only for the FCC and the taxpayers, but also for game theory (and game theorists)." Forbes said, "Game theory, long an intellectual pastime, came into its own as a business tool." The Wall Street Journal said, "Game theory is hot." The government auctioned licenses to use the electromagnetic spectrum for personal communications services (PCS): mobile telephones, two-way paging, portable fax machines, and wireless computer networks. Thousands of licenses were offered, varying in both geographic coverage and the amount of spectrum covered. The bidders were the local, long-distance, and cellular telephone companies, as well as...

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

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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.