Walrasian's Characterization and a Universal Ascending Auction

We introduce a novel characterization of all Walrasian price vectors in terms of forbidden over- and under demanded sets for monotone gross substitute combinatorial auctions. For ascending and descending auctions we suggest a universal framework for finding the minimum or maximum Walrasian price vectors for monotone gross substitute combinatorial auctions. An ascending (descending) auction is guaranteed to find the minimum (maximum) Walrasian if and only if it follows the suggested framework.