Remark 2. That Condition (R) is often not very restrictive suggests that the particular notion of collusion-proofness does not play a significant role. In particular, the second-best outcome is SCP implementable whenever it is WCP implementable if the cartel is all-inclusive or if an additional reasonable condition holds. This suggests that the seemingly pessimistic result of Dequiedt (2007) is not attributable to the cartel’s ability to punish a defector, but rather to the binary type structure of his model. In fact, with the binary type, our weak collusion-proof notion would have led to the same result as his. By our Exclusion Principle, a WCP auction must always exclude the low type, but this means that the seller can never do better than selling the good at the price equal to the high valuation. Theorem 6 suggests that, given non-binary types, the seller can typically do strictly better than this even when the cartel can commit to punish the defector (as has been assumed in our SCP notion).