The number 99 isn’t unique—this works with any payoff between 30 and 100.
Actually, it only works with payoffs below 99.3 -- this is the payoff you get by setting the dial to 30 every round while everyone else sets their dials to 100, so any Nash equilibrium must beat that. This was mentioned in jessicata’s original post.
Incidentally, this feature prevents the example from being a subgame perfect Nash equilibrium—once someone defects by setting the dial to 30, there’s no incentive to “punish” them for it, and any attempt to create such an incentive via a “punish non-punishers” rule would run into the trouble that punishment is only effective up to the 99.3 limit.
Actually, it only works with payoffs below 99.3 -- this is the payoff you get by setting the dial to 30 every round while everyone else sets their dials to 100, so any Nash equilibrium must beat that. This was mentioned in jessicata’s original post.
Incidentally, this feature prevents the example from being a subgame perfect Nash equilibrium—once someone defects by setting the dial to 30, there’s no incentive to “punish” them for it, and any attempt to create such an incentive via a “punish non-punishers” rule would run into the trouble that punishment is only effective up to the 99.3 limit.