If the AI is at war and a resource starbase is destroyed, I can use a constructor to grab the starbase. The AI should sometimes demand that I hand over the starbase. Similarly, the AI should sometimes grab a resource when I just destroyed the starbase. Then, I should have the ability to demand the starbase. I should be able to demand that the vacated resource belongs to me. Of course, the AI will look at the military power and relations before making or accepting demands.
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I don't agree with the approach of letting the AI claim pseudo-ownership of a vacant resource. You park a starbase there, it's yours no questions asked. For every time I've nabbed a resource previously owned by the AI, I've had AIs nab "my" resources after some other AI blew all my starbases up. The solution, if there even needs to be one, is to make the AI better about guarding key starbases and perhaps trying this tactic themselves.
As for more variety in AI initiated trades, I would be hesitant to encourage this. The AI would need to be making good offers in your eyes, or it would just become an annoyance. "No, I told you a million times: I will not sell that starbase for any price!"
~SDC~