Innovations in the design of bundled-item auctions.

A uctions have captured the attention of economists for several reasons. One is the relevance for specific applications of research on auctions in light of their widespread and growing use in the field, particularly in online transactions. Auctions are also highly amenable to economic analysis, because the rules are generally precisely defined; modern game-theoretic techniques of economic analysis can be brought to bear with fewer simplifying assumptions than for many other areas of economics. Furthermore, the rich variety of possible auction rules and underlying environments in which auctions can be conducted provide a wealth of interesting economic issues to investigate. The study of auctions, which began with the seminal work of Vickrey (1), has yielded useful policy prescriptions with regard to the sale of goods. The work that Porter et al. (2) report and summarize in this issue of PNAS is representative of a particularly interesting and useful branch of this research, the development of combinatorial auctions. The Porter et al. (2) study employs the research methodology of experimental economics. Although introduced later than in the natural sciences and psychology, experimental methods in economics have gained broad acceptance in recent decades. As in the natural sciences, an experiment involves constructing a laboratory environment specifically for the purpose of addressing research questions. Human subjects are placed in a laboratory economy, and their decisions and the resulting outcomes are studied. The investigator is able to observe variables with values that are unknown in typical economic situations, to control parameters of interest, and to replicate the experiment repeatedly under identical conditions. One of the most innovative uses of the methodology has been to design and test new auction rules for use in specific applications. The performance of an auction system is typically evaluated on two criteria: efficiency and revenue. Economists generally view an allocation of an item to the potential buyer who receives the highest value from obtaining it, and is therefore willing to pay the most for it, as a desirable outcome. This allocation is termed the efficient outcome. The other criterion, particularly important to sellers, is the revenue the auction generates. Experiments allow precise measurement of these variables and thus enable comparisons of the performance of different systems under otherwise identical conditions. Although the primary research focus has been on auctions of a single item, many existing auctions involve the sale of multiple items. Considerable progress in theoretical modeling has been made for cases where all the goods sold are identical and the value of obtaining extra units does not increase as one obtains more (3–5). Auctions for government debt, produce, hotel rooms, or airplane tickets often have this property. Experimental work has explored the properties of various auction types for this case (see, for example, refs. 6–9).