Edit: This looks like a good description of the process itself, and explains why the problem is difficult and requires the government to be a middleman. https://www.pnas.org/content/114/28/7202
I don't know if this specific auction is listed, but on the whole the auctions are generally the same. There are two types of Auctions: Simultaneous Multi Round (SMR) and Clock. The rules vary between those two Auctions significantly. SMR auctions are an older model, and clock auctions are more common in recent years, though SMR auctions are not completely dead.
Promarket has more articles as well.
Here's the entirety of their explanation:
> SMITH: We've been using this metaphor of a superhighway in the sky. And you know how whenever someone wants to build a superhighway in the real world, there's always some run-down farmhouse in the way that the government has to pay way too much money for? The private equity firms had essentially bought all these key farmhouses blocking the new spectrum highway.
> ROMER: But the plan was not to stop the highway, to block the auction altogether. It was just to make it more expensive. Private equity and their consultants figured out which frequencies the FCC's computers valued the most, the frequencies you really needed to make the whole reorganization work. Once you had those, you could drive up the prices for all the TV stations, which private equity happened to own a lot of.
What reorganization? That's the first time it was mentioned. Why are some frequencies more valuable? (Or alternatively, why is it surprising and non-obvious that some are more valuable). Why would owning stations at these specific frequencies allow you to drive up the other prices?
Edit: you could probably also read the publications on two-sided simultaneous incentive auction and the associated nobel prize that was awarded for this.
To make this possible, there were three basic possible outcomes for a TV station.
1. Get bought out at a price you are happy with.
2. Keep your frequency.
3. Have your frequency replaced with something equivalent (capable of teaching 99.5% of your current potential audience)
With that last point being the key. Even if you happened to own a bit of frequency that was needed for mobile networks, it should not allow you to extract any extra money from the system since you'd just get another frequency slice instead.
How do you game this? Obviously if you own all, or almost all, of the frequencies in one geography you can just set your own price, and the third option will not trigger since there is no equivalent frequency for them to swap you with. But that's just a run of the mill market cornering scenario, and the narrative was selling this as something a lot more interesting, so there is probably more to the story than that.