An Auction with Approximated Bidder Preferences - When an Auction has to be Quick

This paper presents a combinatorial auction which is of particular interest when short completion times are of importance. It is based on a method for approximating the bidders' preferences over two types of items when complementarity between the two may exist. The resulting approximated preference relation is shown to be complete and transitive at any given price vector. It is shown that an approximated Walrasian equilibrium always exists if the approximated preferences of the bidders comply with the gross substitutes condition. This condition also ensures that the set of approximated equilibrium prices forms a complete lattice. A process is proposed which is shown to always reach the smallest approximated Walrasian price vector.