First, we have only examined VCG multi-unit auctions. Similar analysis can be done for other auctions, such as combinatorial auctions or the GSP (Generalized Second Price) auction common in sponsored search auctions. We believe collusion can have a strong effects in sponsored seach, with a significant market impact. Second, We have assumed diminishing marginal valuations of additional items, and it may be interesting to analyze domains where this does not hold. Finally, we have assumed the colluders completely trust each other. It may be interesting to model situations where the trust is only partial. For example, colluders may not de- sire collusion schemes that require item transfers or large monetary transfers. Such distrust may help stop collusion.