Once you have this, you can use it at the first intersection. But at the other intersections, you have some choices
It is a part of the problem statement that you can’t distinguish between being at any of the intersections. So you have to use the same algorithm at all of them.
either recalculate the planning-optimal solution each time
How are you getting this from their words? What about “this coordination can take place only before he starts out at the planning stage”? And “If he chose something else, or nothing at all, then at the action stage he will have some hard thinking to do”? Why would they say “hard thinking” if they meant “recalculate the planning-optimal solution”? (Especially when the planning-optimality calculation is simpler than the action-optimality calculation.)
It is a part of the problem statement that you can’t distinguish between being at any of the intersections. So you have to use the same algorithm at all of them.
How are you getting this from their words? What about “this coordination can take place only before he starts out at the planning stage”? And “If he chose something else, or nothing at all, then at the action stage he will have some hard thinking to do”? Why would they say “hard thinking” if they meant “recalculate the planning-optimal solution”? (Especially when the planning-optimality calculation is simpler than the action-optimality calculation.)