AI Ransom

[Martok]

Sometimes the AI refuses them, in which case you get a message saying the AI refused them and you no longer have to worry about the prisoners (or something to that effect). I assume in that case the AI 1) doesn't have money to pay a ransom 2) or doesn't care about those particular prisoners 3) or both

It's the first one. The AI will always pay the ransom if it can afford it, even if it's only for captured peasants.

have had even a king and other royal family members not paid for, so I didn't net any income from nabbing them.

Yep, that can be very frustrating. You have visions of a 20,000+ ransom dancing through your head, only for the faction in question to be broke....