I can only speak about those that are policy-preserving for a particular player (me).
(In retrospect, I should have maybe been optimising for fun-preserving instead, though policy-preserving is important if you spend a lot of time playing against people of drastically different skill levels, you don’t want to unlearn how to play the game correctly when you’re back to playing a normal game).
That being said,
unit or building costs are higher/resources are slower to gather.
I think if you scaled the cost of everything up by x1.5 or so, it would ruin my build order (though I suppose I could just learn one for the new costs), and I also might have to play more aggressively (as in the late game you’d be at a severe disadvantage). For the same reason, the enemy would be incentivised to play defensively and focus on economy. So I think this fails policy-preservation, but I still think this would be a reasonable handicap, and it’d still be fun for both sides.units move slower
This would really mess things up. An enemy gets to now choose which engagements they want, archers can no longer hit-and-run infantry, enemy siege would be proportionally too fast, ect. I think this would break core mechanics of the game, or at least drastically shift show I would play (probably overly reliant on units that can move quickly like cavalry, or play heavy defense).units are proportionally weaker but maintain the same ordinal ranking of what they are vulnerable to and strong against
What you mean by “weaker”, do my units deal less damage, or do they have less health? In the first case, I would probably focus more on ranged units to either push the exponent of Lanchester’s Law[1] closer to 2 in the case of less damage (as for any melee battle I’ll not be able to win without drastically overproducting units) or for the latter, focus mainly on units with the ability to hit and run (cavalry archers, conquistadors, ect.) or for which their lack of health is already offset by something else (monks, siege).
For large armies this would mostly average out, but since units deal a discrete amount of attack, and units have a discrete quantity of health points, the thing that matters for very small numbers of units is “number of attacks to kill”, so unfortunately the effect on the game would vary discontinuously with a health penalty adjustment. I don’t see why the enemy couldn’t just waltz over very early and cripple me near the start of the game.
It would probably still preserve fun though.units or buildings take longer to build
It would make for a frustrating penalty to play with, and I would play defensively until I could get enough production buildings running. But I think a modified version of this where I have a limit on the number of production buildings I’m allowed to make, or on the number of villagers I’m allowed to have, might better preserve policy.
Of these, I think the third option is probably the best for game balancing (as it’d be easy to dial in the penalty as needed), but the fourth would (at least for me) would probably be the most policy-preserving.
[1] https://en.wikipedia.org/wiki/Lanchester%27s_laws
AIXI isn’t isn’t a practically realisable model due to its incomputability, but there’s nice optimality results, and it gives you an ideal model of intelligence that you can approximate (https://arxiv.org/abs/0909.0801). It uses a universal Bayesian mixture over environments, using the Solomonoff prior (in some sense the best choice of prior) to learn, (in a way you can make formal) as fast as possible, as fast as any agent possibly could. There’s some recent work done on trying to build practical approximations using deep learning instead of the CTW mixture (https://arxiv.org/html/2401.14953v1).
(Sorry for the lazy formatting, I’m on a phone right now. Maybe now is the time to get around to making a website for people to link)