Here are some fun stories

I came across during my research on collusion in auctions, from "Bidding Markets" by Oxford economics professor Paul Klemperer:

One of the biggest problems faced by firms who wish to collude or predate is how to signal their intentions to rivals when ordinary communication is illegal. Unfortunately for regulators, the formal rules of auctions often solve firms' problem by defining a "language" that bidders can use to communicate with each other.

Klemperer (2002a) gives many examples, including a multi-license US spectrum auction in 1996 to 1997, in which US West was competing vigorously with McLeod for lot number 378 — a license in Rochester, Minnesota. Although most bids in the auction had been in exact thousands of dollars, US West bid $313,378 and $62,378 for two licenses in Iowa in which it had earlier shown no interest, overbidding McLeod, who had seemed to be the uncontested high-bidder for these licenses. McLeod got the point that it was being punished for competing in Rochester, and dropped out of that market. Since McLeod made subsequent higher bids on the Iowa licenses, the "punishment" bids cost US West nothing (see Cramton and Schwartz, 2000).

This is at page 16 (paragraph break added, footnote omitted). Also, from page 17, footnote 54:

Another favourite example of bidders' ability to "collude" in a "one-off" ascending auction was provided by the 1999 German DCS-1800 auction: ten blocks of spectrum were sold, with the rule that any new bid on a block had to exceed the previous high bid at least 10 per cent. There were just two credible bidders: the two largest German mobile-phone companies, T-Mobil[e] and Mannesman[n]; and Mannesman[n]'s first bids were DM18.18 million per megahertz on blocks one to five and DM20 million per MHz on blocks six to ten.

T-Mobil[e] — who bid even less in the first round — later said "There were no agreements with Mannesman[n]. But [we] interpreted Mannesman[n]'s first bid as an offer" (Stuewe, 1999, p. 13). The point is that 18.18 plus a 10 per cent raise equals 20.00. Clearly T-Mobil[e] understood that if it bid DM20 million per MHz on blocks one to five, but did not bid again on blocks six to ten, the two companies would then live and let live with neither company challenging the other on the other's half. Exactly that happened. So the auction closed after just two rounds with each of the bidders acquiring half the blocks for the same low price, which was a small fraction of the valuations that the bidders actually placed on the blocks.

This is how to have fun with secret decoder rings!

UPDATE: Klemperer adds (p. 18) that the danger of such collusion can be exaggerated. "[B]idders often seem more imaginative in their attempts to signal than in their understanding of others' signals — as usual, something is much more obvious after it has been explained."

First footnote (59): "It is often entertaining to hear after an auction what bidders thought they were communicating. Though I'm not sure I fully believe the southern European bidding team who explained that its bid in a major auction had an obvious interpretation from the Bible, the dumbfounded and horrified reactions of the northern European consultants who had spent considerable effort trying to decode the bid at the time were a treat to behold. Culture matters."

Second footnote (60): "Another problem is when there is more than one bidder who thinks it is, or should be, the leader coordinating the others. See Klemperer (2002d, 2003a)."