Influence starbase effect

Your right about inf SB's being used to flip planets to your side.I find  If other's build inf SB's near your world(s) it has little effect if there deep inside your territory or SOI (sphere of influence),

how ever if your colonies sit on the border with a race which has stronger influence than you or is actively trying to increase its inf by building SB's I find that researching the various cultural and influence techs helps a little I also build SB's and upgrade them after I have done the research, this helps keep enemy inf near my border colonies down.

If you can early on in the game build the restaurant of eternity it gives a 20% inf boost overall. If you attack an enemy inf base it will be a declaration of war, and if that race has allies they may attack you as well and your relation's with other races may suffer somewhat. so don't rush with guns blazing fight inf with inf its long process but can be more effective than all out war.

The other option is get another race to declare war on them if they do then star-bases are usually the 1st to be attacked.

I'm not so good with a cultural strategy as i favour war and manipulation and the occasional bit of genuine  diplomacy as my general strategy, but I hope what little I do know helps your game. Browse the forums they have a alot of hints and tips regarding inf and "culture war".

The SBs that I see the AI build the most near my planets are the economic ones, to take advantage of multiple trade routes there.

There are many factors that go into the calculation of influence, including population of the planet, the influence racial rating (increased by research), buildings on the planet, and the empire-wide things like Restaurant of Eternity.  the SBs also can be upgraded to increase influence.

Two other things Influence bases can do are to (1) get an AI to declare war on you, and (2) get that last few % of galaxy needed to achieve influence victory.

I can't recall if one can trade/gift an influence base.  If so, then one might build one beside the planet of one AI then give it to another and see if that leads to a war between them!

Actually you can simply ignore them, the AI usually don't max them out or build them directly toward the planet where they would be more efficient. Also, on a certain time the AI concentrates on weapons-research solely, he's usually not having the techs either to be able to flip your planets with said base.

Yes, you can do that. Nice idea Jim.