Suppose you control the bid prices in a multiple-item VCG auction for a partial coalition of bidders. Each bidder is only allowed to win one item out of the set of multiple items, which are all identical. The number of other participants in the auction who are not part of the coalition is not be known in advance. Each bidder in your coalition may have a different internal value for the item and you want to minimize the cost for your coalition.
How can you take advantage of partial collusion to optimize bidding for your coalition?