I've never seen the AI put any value in the IPs during trade.
Usually the AI doesn't offer or request Influence. But on the contact page, right and left columns, top you can see listings for bc's and Influence. In essence, you can "spend" Influence, buy or sell, the same way you use bc's.
Didn't know that those Influence acquisitions were only temporary. I thought they were simply added to your running total.