The AI doesn't seem to use influence bases aggressively enough so even if they did have the sense to upgrade one, it probably wouldn't help them much.  You can pretty much rule the AI out as a serious contender for influence victories.

I have seen games where the AI would place influence starbases near other people's (even my) planets. So sometimes they're able to make use of them, but it is of no use if they don't upgrade them.

Yes I believe the AI only uses modules from the diplomacy branch, and I've never seen them go past the first two, except for the minors. Even if I give them the culture techs, they don't use the modules on the starbases. The AI seems to enjoy economic starbases the most, followed by military ones, which it develops fairly well.

I've seen all races build influence starbases, so I don't think the race matters. But indeed on a smaller map they seem to build influence starbases more often, but to no use, since they're almost always left without modules.

Do they also upgrade them to potentially pose an actual threat? In a 1v1 game against the Krynn they placed 2 influence starbases near my homeworld, but failed to upgrade them.

Removing the influence branch modules all together and upping the government branch ones to compensate might work. The only problem would remain in the AI not using race-specific modules, like the Thalan or the Krynn ones, but I probably could live with that, if the AI would competently upgrade its influence starbases.

However, before I begin doing this, I need to further test-play to observe current AI behavior.

I actually took qrtxian's word, and modified my files so there are only 4 influence modules available, all on the diplomacy branch, except for the race-specific ones (Krynn and Thalan). I made them powerful and expensive, and also made the techs expensive. They're balanced because they're very powerful, but fully upgrading a starbase will cost you close to 2000bc.

I've made many test-plays today and I've seen games with no influence starbases at all, games with plenty but not upgraded, and games with a few ones upgraded. It seems very random. I made these tests by using the CTRL+Z cheat and watching the AIs develop.

I'll look at your starbase XML MarvinKosh, maybe I'll learn something. Although your mod changes the techtrees so drastically that the behavior you describe might be attributed to something else, rather than the StarbaseModules.xml.

EDIT: Your StarbaseModules.xml looks pretty vanilla, except for the inverse order you mentioned. I'll try that.

EDIT2: Also, playing with CTRL+Z isn't the most reliable method of testing, since the AIs have little time between turns to think ahead, and sometimes the AIs seem to go full retard. But I don't really have the time and patience required...

I have a question about efficacy of influence starbases by themselves. For example, I snatched a level 9 planet from Dominion of the Korx in the early phase and then proceeded to fill it up with embasies and also took the trouble to put 4 influence bases in the sector to try and flip remaining 2 planets (level 9 and level 6 or so)... with absolutely zero effect.

The bases were heavily upgraded until the cost of the entire enterprise backfired and got me steamrolled by others.

Korx even have a loyalty handicap, while I did not have any racial bonus (custom civilization).

So... making AI waste effort like this only handicaps them, no?

I have to share this rare moment of which I am quite proud. Playing as the Torians, I've seen the Thalan engage in influence warfare.

You will notice that the starbase modules are not vanilla ones, they are modified ones, fewer, more powerful and expensive to build. They are all in the Diplomacy branch of the tech tree. The 35 one is the default one available to everyone, the 55 one corresponds to the Diplomatic Relations tech, and the 80 one corresponds to the Expert Diplomacy tech. There's a 100 one that corresponds to the Total Majesty tech that the AI didn't build. The Thalans also have their race-specific modules that they also didn't build. But even so, these 3 modules that they built put together add up to a total of +170% influence, which is great. Also notice that the starbase is actually in range of my planets. It was built when only one of those planets was mine. Other AIs have also built influence starbases but haven't upgraded them. They do seem to be the lowest priority when upgrading starbases.

PS: It might be possible to make the AI improve their influence starbases more if there are fewer starbase modules to build, so their constructors will finish improving other starbases faster. It would also make improving starbases less daunting even for the player. I have reduced their number quite a lot already, but I haven't touched the mining and the production modules because there are so many, it's hard to decide how to spread them out. Maybe I'll give it a shot at some point and report back.

My effort to solve the problem was to eliminate costs for all starbase modules.  Since the AI lacks any ability to budget or plan for the next turn, they often don't have the cash to upgrade a starbase when the constructor gets there.  Then they either pick a free upgrade or turn around and go elsewhere.  This is more critical with AIP 11, because there is only a brief window between the colony rush and militarization where the AI will build lots of constructors.  Miss that window, and the chance of having random influence bases upgraded declines sharply.  AIP 8 loves it some starbases, though, so I think it is less of a problem for them.

Also, for playtesting, I gave up on autoplay long ago.  Instead, take over a minor race, use the research cheat to get all the techs, build up your planet and make a few guardian ships to deter aggression.  Drop out of the UP and just keep ending your turn.  It's a much better way to watch things develop, and not prone to disaster like autoplay.