T here is interest in designing simultaneous auctions for situations such as the recent FCC radio spectrum auctions, in which the value of assets to a bidder depends on which other assets he or she wins. In such auctions, bidders may 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 difficult. We analyze this problem, identifying several different structures of permitted combinational bids for which computational tractability is constructively demonstrated and some structures for which computational tractability cannot be guaranteed.

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In analyzing bidding, modeling matters. This paper is a critical analysis of the models available to aid competitive bidding decision making---bidding strategy and auction design---in real transactions. After an introductory overview, this paper describes the contexts in which auctions arise, reviews the "mainstream" theory of single, isolated auctions and discusses the important work involved in enrichment of this theory. In doing so, it indicates results that have been obtained and the sort of changes in analytical approach that are needed to tackle other critical enrichments. The paper summarizes briefly what is known about the direct use of models by bidders and auction designers. A general theme of this paper is that enriched models are needed to bring bidding theory closer to direct applicability in decision making.games--group decisions, bidding--auctions, modeling, economics, decision analysis

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