The thing about AK is that it's quite possibly the most overrated hand in NLHE cash games. There are probably several reasons for this, not the least is that it's a hand that you'll virtually never lay down preflop in tournaments - but that's because you're operating with much smaller stack sizes.
I'm obviously not saying that anyone should start looking for folds with AK in ring games, because that's going to be a huge leak. But it's important to understand how to make the most of it, and while I probably 4bet AK more than nine times out of ten I'm dealt it and someone 3bets me, the "why" is never, ever, "value." Not if you define a value bet as something that has positive expectation when called, and 4bets with AK most certainly don't - not versus other regs, at least.
So is it a bluff? In some sense, it is. What makes 4betting with AK so special is that you are - typically - ahead of your opponent's range with the hand when he 3-bets, but his range obviously changes once he decides to shove over your 4-bet. And versus his new range, you're a dog. You're going to have to make a crying call because of the pot
odds, but you're not going in as a favorite versus his range.
Belgo, in the later edited post, called it "picking up the dead money" which is a pretty good way to explain where the value in 4-betting AK comes from. It's a situation not entirely unlike betting with JJ on a K-Q-x board, because we're probably ahead when we make the bet but we're behind when the other guy doesn't fold. An important difference between the two scenarios is that we're not (typically) forced to call a raise with JJ on that board, but we are committed when we 4bet AK.
Another way to look at it is to adopt a fixed limit perspective. In limit games, it's often correct to raise with hands that rate to be behind your opponent's range when called, but they'll force "incorrect folds" where "incorrect" means that they'll fold a hand that they wouldn't if they knew what you had. For example:
$1/$2 6-max game 100bb effective stack, I open AK UTG to $6. Reg 3-bets to $21 on the button with QJo, and I 4-bet to $50. He's getting about 7:3 on a call, and versus my specific hand, he'd be right to look at a flop. Of course, he doesn't know that, and so he can't call. He has to consider my range, which includes AA and KK versus which he's crushed. He's making a "bad fold" in some Sklanskyan sense, and that means we gain.
Does that make it a bluff? No-limit games usually think of
bluffing as something we do with the worst hand, but limit specialists are pretty used to raising with the best hand to force incorrect folds.
Having said all that, there are times where folding AK preflop is really the best play. Out of position versus a tight 3-bettor is a good example; if the guy in the example above 3-bets only 4% on the button, I have to let it go. I have great equity versus his range, but 4betting will only lead to me getting stacks in versus a range I can't beat, and while he might certainly make "bad folds" if I raise, he doesn't have enough hands in his range to make up for the times that I stack off. I also can't call, because I have severely negative implied odds. In position versus a really tight 3-bettor, it's often fine to just flat AK and give up when you miss, but out of position there's no shame in folding it.