In combinatorial auctions, a large number of items are auctioned concurrently and bidders are allowed to express preferences on bundles of items. This is preferable to selling each item separately when there are dependencies between the different items. This problem has direct applications, may be viewed as a general abstraction of complex resource allocation, and is the paradigmatic problem on the interface of economics and computer science. We give a brief survey of this field, concentrating on theoretical treatment. Introduction A large part of computer science as well as a large part of economics may be viewed as addressing the “allocation problem”: how should we allocate “resources” among the different possible uses of these resources. An auction of a single item may be viewed as a simple abstraction of this question: we have a single indivisible resource, and two (or more) players desire using it – who should get it? Being such a simple and general abstraction explains the pivotal role of simple auctions in mechanism design theory. From a similar point of view, “combinatorial auctions” abstract this issue when multiple resources are involved: how do I allocate a collection of interrelated resources? In general, the “interrelations” of the different resources may be combinatorially complex, and thus handling them requires effective handling of this complexity. It should thus come as no surprise that the field of “combinatorial auctions” – the subject of this chapter - is gaining a central place in the interface between computer science and economics.
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© Noam Nisan, Tim Roughgarden, Éva Tardos, Vijay V. Vazirani 2007.