Kidane Asrat Ghebreamiak
ABSTRACT
Combinatorial Auctions are preferable to traditional (sequential) auctions since they allow bidders to express complementarity and substitutability relationships between items, and hence may enhance economic efficiency. However, in such auctions, the problem of determining the optimal winning bids is \textitNP-hard in the general case. In a recent paper, Leyton-Brown et al. have proposed an algorithm for computing the winners in a multi-unit combinatorial auction. It is a branch and bound algorithm that makes use of a caching technique. In this note, we present a counterexample to show that caching, as described by the authors, may fail and the algorithm may eventually give a suboptimal solution. We discuss why it fails and propose how it could be fixed and properly used in a General (multi-unit) combinatorial auction.
- Fujishima, Y., Leyton-Brown, K., Shoham, Y. 1999. Taming the computational complexity of combinatorial auctions: optimal and approximate approaches. In Proceedings of the Sixth International Joint conference on Artificial intelligence, IJCAI-99. Google Scholar
Digital Library
- Leyton-Brown, K., Shoham, Y., and Tennenholtz, M. 2000. An algorithm for Multi-unit Combinatorial Auctions. AAAI-00. Google ScholarDigital Library
- Nisan, N. 1999. Bidding and allocation in combinatorial auctions. Working paper.Google Scholar
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- Sandholm, T. 1999. An algorithm for optimal winner determination in combinatorial auctions In Proceedings of the Sixth International Joint conference on Artificial intelligence, IJCAI-99. Google ScholarDigital Library
- Sandholm, T. 2000. Approaches to Winner Determination in Combinatorial Auctions Decision Support Systems. 28,1--2, 165--176. Google ScholarDigital Library
- Sandholm, T., and Suri. S. 2000. Improved Algorithms for Optimal Winner Determination in Combinatorial Auctions and Generalizations National Conference on Artificial Intelligence (AAAI). Google ScholarDigital Library
- Vries, S., and Vohra, R. 2001. Combinatorial Auctions: A Survey. Unpublished manuscript. (http://www-m9.mathematik.tu-muenchen.de/devries).Google Scholar
Index Terms
- Caching in multi-unit combinatorial auctions
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