After six long weeks of studying single-parameter auctions to death!, we are ready to move on to the study of multi-parameter auctions. In single-parameter auctions, there was sometimes a single good, and sometimes more than one good (e.g., sponsored search), but the bidders were always characterized by but one parameter. Auctions in which there are multiple (indivisible) goods, and the bidders...

We study the computational power of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their “demand” under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natur...

This chapter concerns the issue of the representation of bids in combinatorial auctions. Theoretically speaking, bids are simply abstract elements drawn from some space of strategies defined by the auction. Every implementation of a combinatorial auction (and, in fact, every other game) must define how each possible bid is actually represented using the underlying communication technology. As t...

Motivated by the increasing use of auctions by government agencies, we consider the problem of fairly pricing public goods in a combinatorial auction. A well-known problem with the incentive-compatible Vickrey-Clarke-Groves (VCG) auction mechanism is that the resulting prices may not be in the core. Loosely speaking, this means the payments of the winners could be so low, that there are losing ...

Despite the large amounts of runtime needed to adequately solve a combinatorial auction (CA), existing iterative CA auction protocols require winner determination during every round of bid submissions. Using existing algorithms for winner determination will cause a timing bottleneck during the winner determination phase. Furthermore, there has recently been work which models the formation of su...

Combinatorial auctions (CAs) have been studied by the multiagent systems community for some time, since these auctions are an effective mechanism for resource allocation when agents are self-interested. One challenge, however, is that the winner-determination problem (WDP) for combinatorial auctions is NP-hard in the general case. However, there are ways to leverage meaningful structure in the ...

This paper analyzes ex post equilibria in the VCG combinatorial auctions. If Σ is a family of bundles of goods, the organizer may restrict the bundles on which the participants submit bids, and the bundles allocated to them, to be in Σ . The Σ-VCG combinatorial auctions obtained in this way are known to be truth-telling mechanisms. In contrast, this paper deals with non-restricted VCG auctions,...

Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes, network routing and furniture. Because of complementarities or substitution effects between the different assets, bidders have preferences not just for particular items but for sets of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles o...

Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes, network routing and furniture. Because of complementarities or substitution effects between the different assets, bidders have preferences not just for particular items but for sets of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles o...