Frederik Spieksma

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 combinatorial 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 satisfies 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.

A Note on Peer-to-Peer Satellite Refueling Strategies

We revisit the peer-to-peer refueling problem, in which the maneuvering satellites are allowed to interchange their orbital positions [2]. We show that the problem is computationally hard, by reducing it to a special case of the three-index assignment problem. On the positive side, we show that the size of instances from practice is such that a state-of-the-art integer programming solver is able to find optimal solutions in little computing time.