Hello Junhyuk,
I trust you are well, and thank you for your reply,
The natural first future-work item you may consider extends exactly from your “attackers can hold dark capacity too” argument:
Symmetry there is granted, a conclusion, not an assumption. However, if hidden capacity favours attack or defence can only be settled by modelling the contest: a block-level double-spend race — the next order up from the transaction-level race — which escalates into a bidding war for the capacity itself, the order above that. It is a game, and someone should model it.
The foils already exist, and they bind even if nobody does:
- Budish (QJE 2024) models the double-spend contest with a fixed acceptance rule and no reactive defender. The doomsday bounds follow from that assumption.
- Bonneau (FC’16) and Bonneau et al. (FC’18) model attack-capacity rental and acquisition — again with no strategic defender on the other side of the market.
- Moroz, Aronoff, Narula & Parkes (2020) is the exception that proves the pattern: the moment the victim can counter-fork, deterrence emerges and the attack is not attempted.
Remove the defender’s move and you get collapse; restore it and you get deterrence. Your paper inherits the first family’s assumption. That is a legitimate scope choice — but it should be cited as one, because these foils bound your claims whether or not the game is in scope.
So, stated as a referee would: either model the contest, or cite these foils and state explicitly that the deviation results hold only under the no-reactive-defender assumption they share.
Kind Regards, Cameron