Walrasian's Characterization and a Universal Ascending Auction

TL;DR

This paper presents a new characterization of Walrasian prices using forbidden sets and introduces a universal ascending auction framework that guarantees finding extremal Walrasian prices in monotone gross substitute combinatorial auctions.

Contribution

It provides a novel characterization of Walrasian prices and a universal auction framework ensuring convergence to extremal prices in such auctions.

Findings

Characterization of Walrasian prices via forbidden sets

Universal ascending auction framework guarantees extremal prices

Framework applies to monotone gross substitute combinatorial auctions

Abstract

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.