BOB: Improved winner determination in combinatorial auctions and generalizations.

*(English)*Zbl 1082.68813Summary: Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary or substitutable. Determining the winners is NP-complete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper presents a more sophisticated search algorithm for optimal (and anytime) winner determination, including structural improvements that reduce search tree size, faster data structures, and optimizations at search nodes based on driving toward, identifying and solving tractable special cases. We also uncover a more general tractable special case, and design algorithms for solving it as well as for solving known tractable special cases substantially faster. We generalize combinatorial auctions to multiple units of each item, to reserve prices on singletons as well as combinations, and to combinatorial exchanges. All of these generalizations support both complementarity and substitutability of the items. Finally, we present algorithms for determining the winners in these generalizations.

##### MSC:

68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |

91B26 | Auctions, bargaining, bidding and selling, and other market models |

91A46 | Combinatorial games |

##### Keywords:

Auction; Combinatorial auction; Multi-item auction; Multi-object auction; Bidding with synergies; Winner determination; Multiagent systems##### Software:

CABOB
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\textit{T. Sandholm} and \textit{S. Suri}, Artif. Intell. 145, No. 1--2, 33--58 (2003; Zbl 1082.68813)

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##### References:

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