When I take a look at my neighborhood, I see all IP have this bonus :

The value doesn't stack with time, and I think it's because I didn't sign the first treaty.

But when I sign the first treaty, I don't have the +1 Shared Influence bonus anymore

Save : Elphealer.ctr

Regards,
Elphy

Yup, I saw this thing yesterday as well. It said I had like 0.5 due to shared influence when not having signed any treaty (although it did not move the bar and did not raised anything, since I had not even introduced myself to them), so maybe just a display bug, then I signed a treaty and suddenly it showed I gained 0 influence and had to spend influence or money to start gaining any.