Computationally manageable combinational auctions

There 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 non-conflicting 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.