Will there be competition between rogue AI's? Once one is made, there will soon be others in competition with it - this will lead to a death struggle between mo

Will there be competition between rogue AI's? Once one is made, there will soon be others in competition with it - this will lead to a death struggle between more and more AIs. Will the winning AI, if there is one, look on animals as pets? Will they breed people like we breed greyhounds? Will the top AI advance to become dominant and make more of itself to the point where the earth has one hive mind of an AI? They will engage in different form of competition to humans, no more sex/food wars - once one wins it might have an IQ of, say 4 million and will be coupled with more or less infinite memory and have a cycle time in the dozens of gigahertz AND be massively parallel. Are the stars owned by such AI's? Do they own large areas, expanding star by star, still limited by light speed. Will two such AI's ever meet and make war or will they rationally decide which way is the superior AI mind, and will the inferior one see the better ideas of the better one and adopt them? Conversion beats conquest in resource gathering. Will religion emerge and wars to the death occur between the two AI systems?