You often get those kind of problems when playing strategy games, especially 4X (civ-like) games, with developing your cities/bases vs producing military units. The main difference with your “toy problem” is that in games the N isn’t fixed, but probabilistic, which makes it much harder.
I often tend to spend most of the time developing my production capacity (as you said, it’s the most efficient thing to do with a fixed N) but sometimes I do it too much and I get caught unprepared by an attack...
You often get those kind of problems when playing strategy games, especially 4X (civ-like) games, with developing your cities/bases vs producing military units. The main difference with your “toy problem” is that in games the N isn’t fixed, but probabilistic, which makes it much harder.
I often tend to spend most of the time developing my production capacity (as you said, it’s the most efficient thing to do with a fixed N) but sometimes I do it too much and I get caught unprepared by an attack...
Yup, what immediately came to mind when I started reading the post were CMS & 4X games like Hamurabi & Civilization.
I expect the simplest way to handle a probabilistic N is to apply a discount factor to future utility. (It’s what the Freeciv AI does.)