In the case of United States v. Carollo, Goldberg and Grimm (municipal bond bid rigging), the losing bidders thought they were participating in a Dutch auction (first-price sealed bid). The rigged winning bidder, being able to see all the other bids, was participating in an English auction (second-price sealed bid, or Vickrey auction).
Bidding strategies are different between Dutch and English auctions. If the losing bidders knew they were in an English auction, they would have bid higher, which would have gained municipalities better interest rates.
This is where the harm occurred, and why the bid rigging was not fair as the defendents tried to assert. The mechanism is sufficiently subtle that perhaps even they didn't even realize how much harm it was causing.
Rolling Stone wrote a sensational article about this case but completely missed this point.
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