Thought experiment assumptions:
A) There is only one exchange with one nsr/nbt pair on it.
B) The tllp there has a 10 nbt dual side target and 0.1%/day compensation
C) Lucy is the only person who uses tllp, and she is providing dual side support of 10 nbt to each side.
D) Market demand for nsr is exactly $0.1.
E) Nu prints $0.1 nbt daily and there are 100 nbt in existence, 80 of which are in the hands of trusted people (not including Lucy)
F) There is 0 market demand for nbt.
Every day, people will submit to the auction with a 10:1 ratio of NSR:NBT. This is because market demand is exactly $0.1 and nbt is pegged to $1, so if the auction price deviates from $0.1 at all and you submitted 10:1, then you win.
People sell some NBT to lucy for her NSR, but they sell it onto her wall, so she gets the NBT cheap from her spread. So let’s say she lost 10 of her 100 NSR and gets 1.01 NBT in return. She now puts that 1.01 NBT up to auction.
So now the auction, feeling the low NBT demand, seeds 10 NSR. People submit let’s say 30 NSR and 3 NBT. Lucy submits 1.01 NBT. The auction closing price is: 4.01/40 = $0.10025. Lucy receives 9.97 NSR which she puts back up on the buy wall. As long as this only happens every 3 days, she makes money off this process via the custodial grant.
The result of this is that Nu gets to sell its NSR directly to Lucy for relevant prices without having to trust Lucy at all. This is exactly the intent of our current weekly auctions. Here it works beautifully and uses the tllp incentive as a direct financial consequence of not using the auction to balance the peg.