By influence. Everytime I go for military win and don't focus on influence the top AI starts grabbing my systems. The AI seem to rule culturally and militarilly. They're like jack of no trades master of all  Any suggestions? It was really bad at "Intelligent" but has happened at lower intelligence levels too.
     
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you could try to build cultural influence Starbases in your sectors.
Keeping the moral helps to keep the colonis on your side too.
Try to avoide to have their colonies in your sector!
       
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Until you get down the process of grabbing the influence wonder anf TGs before the AI, trying getting an influence bonus pick at the beginning of the game.
  
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Colonize where you can have 2 or more systems in a sector when possible. They can eat the empty sectors around you but you hold on to your little island of influence.
 
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