An algorithm for clearing combinatorial markets
Nzouonta, Josiane Domgang
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It was recently shown possible to solve single item auctions without revealing any secret except for the solution. Namely, with vMB-share , the seller and the buyer only learn each other's identity and the selling price for a chosen M+1 pricing scheme. No trusted party was necessary. In this thesis, we show how vMB-share can be extended for the clearing of combinatorial negotiations with several items, buyers and sellers. We first show how the more general problem can be reduced to a virtual form, relatively similar to the single-item auctions. Then, some modifications in the cryptographic techniques of vMB-share are made such that it can offer a solution to problems in virtual form. While the problem is known to be NP-complete, a secure multiparty computation that avoids the secrets leak by measuring computation time necessarily takes an exponential computation cost. Some early experiments show that small realistic negotiations can nevertheless be solved with acceptable effort.