If you are at war with an A.I. empire, it is hard to make peace with them. They usually don't agree to treaty proposals. They will get angrier each time you have a battle with them. If you don't battle them for a long time, their anger level slowly decreases naturally. But it's hard to not fight them if you're at war and they're attacking you. Giving them gifts decreases their anger, but they may not accept the gifts if they are too angry. So I have never been successful in making peace with an A.I. once war has broken out, though I hear that in theory it is possible.
As for the big empire that's making demands: The A.I. isn't very smart. If it makes a demand, it will be satisfied if you reply to it agreeing to the demand, even if you don't follow through. But I think most of consider that to be exploiting the A.I... Anyway, if you are not at war yet with that A.I. empire, try to keep it happy by agreeing with everything it wants, and not attacking any of their ships or planets, and maybe giving it gifts. You can exploit the A.I. by gifting it outdated and damaged ships you don't want, even it it's helplessly stranded in the middle of nowhere.
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