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.

Combinatorial auctions have two features that greatly affect their design: computational complexity of winner determination and opportunities for cooperation among competitors. Dealing with these forces trade-offs between desirable auction properties such as allocative efficiency, revenue maximization, low transaction costs, fairness, failure freeness, and scalability. Computational complexity can be dealt with algorithmically by relegating the computational burden to bidders, by maintaining fairness in the face of computational limitations, by limiting biddable combinations, and by limiting the use of combinatorial bids. Combinatorial auction designs include single-round, first-price sealed bidding, Vickrey-Clarke-Groves (VCG) mechanisms, uniform and market-clearing price auctions, and iterative combinatorial auctions. Combinatorial auction designs must deal with exposure problems, threshold problems, ways to keep the bidding moving at a reasonable pace, avoiding and resolving ties, and controlling complexity.Auction Design, Combinatorial Bidding, Bidding with Synergies

Approval voting, probabilistic choice models, probabilistic ranking models, subset choice,

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