Preliminary notes: You can call me "Wei Dai" (that's firstname lastname). "He" is ok. I have taken a graduate level course in game theory (where I got a 4.0 grade, in case you suspect that I coasted through it), and have Fudenberg and Tirole's "Game Theory" and Joyce's "Foundations of Causal Decision Theory" as two of the few physical books that I own.

Their point is that if you insist on reasoning in this way, (and Seldin's notion of "subgame perfection" suggests some reasons why you might!) then the algorithm they call "action-optimality" is the way to go about it.

I can't see where they made this point. At the top of Section 4, they say "How, then, should the driver reason at the action stage?" and go on directly to describe action-optimality. If they said something like "One possibility is to just recompute and apply the planning-optimal solution. But if you insist ..." please point out where. See also page 108:

In our case, there is only one player, who acts at different times. Because of his absent-mindedness, he had better coordinate his actions; this coordination can take place only before he starts out}at the planning stage. At that point, he should choose p*1 . If indeed he chose p*1 , there is no problem. If by mistake he chose p*2 or p*3 , then that is what he should do at the action stage. (If he chose something else, or nothing at all, then at the action stage he will have some hard thinking to do.)

If Aumann et al. endorse using planning-optimality at the action stage, why would they say the driver has some hard thinking to do? Again, why not just recompute and apply the planning-optimal solution?

I also do not see how subgame perfection is relevant here. Can you explain?

Let me just point out that the reason it is true that "they never argued against it" is that they had already argued for it. Check out the implications of their footnote #4!

This footnote?

Formally, (p*, p*) is a symmetric Nash equilibrium in the (symmetric) game between ‘‘the driver at the current intersection’’ and ‘‘the driver at the other intersection’’ (the strategic form game with payoff functions h.)

Since p* is the action-optimal solution, they are pointing out the formal relationship between their notion of action-optimality and Nash equilibrium. How is this footnote an argument for "it" (it being "recomputing the planning-optimal decision at each intersection and carrying it out")?