The Matrix Bid Auction: Micro-Economic Properties and Expressiveness

A combinatorial auction is an auction where multiple items are for sale simultaneously to a set of buyers. Furthermore, buyers are allowed to place bids on subsets of the available items. This paper focusses on a com- binatorial auction where a bidder can express his preferences by means of a so-called ordered matrix bid. This matrix bid auction was developed by Day (2004) and allows bids on all possible subsets, although there are restrictions on what a bidder can bid for these sets. We give an overview of how this auction works. We elaborate on the relevance of the matrix bid auction and we develop methods to verify whether a given matrix bid satisfles a number of properties related to micro-economic theory. Finally, we investigate how a collection of arbitrary bids can be represented as a matrix bid.