It feels like both you and the previous responder are predicating that there can only be one AI. If there is only one AI then yes, they don't love/hate or care about people and will likely have the resources to use them for their own means.

But, and I am looking for math, science or something more than Sci-fi, that can can show us that there will likely only be one AI, ever. If not wouldn't the AI's also try to manipulate and exploit each other for individual gains?

Perhaps I just don't understand AI well enough but I have yet to see any reasonable evidence that points to only one AI entity evolving on earth. If there are more than one AI then is in unreasonable to think that people may still be able to think thoughts or come up with (emotional and irrational ideas) that the AI could not come up with that give it a competitive advantage over the other AI's? Thereby leading to a more symbiotic relationship between humanity and the AI's.