Influence starbases are overpowered, you don't even need to take Pacifists or +influence abilities. In gigantic universe if you control all the influence starbases then the game is already over..... and AIs will trade all their starbases to you for a few techs or cash, I usually have them all by end of year 1. Well really the mining starbases in general are just insanely overpowered in large, huge, and gigantic universes.
AI's should value starbases about as much as they value their planets or maybe just make the mining ones totally untradeable.