An auction is combinatorial when bidders can place bids on combinations of items, called “packages,” rather than just individual items. Computer scientists are interested in combinatorial auctions because they are concerned with the expressiveness of bidding languages, as well as the algorithmic aspects of the underlying combinatorial problem. The combinatorial problem has attracted attention from operations researchers, especially those working in combinatorial optimization and mathematical programming, who are fascinated by the idea of applying these tools to auctions. Auctions have been studied extensively by economists, of course. 2 Thus, the newly emerging field of combinatorial auctions lies at the intersection of computer science, operations research, and economics.

In this article, we present a brief introduction to combinatorial auctions, based on our book, Combinatorial Auctions (MIT Press, 2006), in which we look at combinatorial auctions from all three perspectives. Indeed, our contribution is to take an integrated and comprehensive approach. We have done this in three ways. First, we have defined what we see as the five major subfields comprising combinatorial auctions: mechanisms, bidding and efficiency, complexity and algorithmic considerations, testing and implementation, and applications. The book is accordingly divided into five sections, with chapters written by the foremost experts on each topic within each subfield. Second, we have defined for the first time a common lan-