Not really sure what you mean by "threatening information to the GK". The GK-player probably cares less about this information than the GK, right? In that case, the GK is given an advantage, not a disadvantage.
As a less extreme example, the AI starts spoiling all the books/tv shows/etc. While the GK would just shrug it off, it also has a negative effect on the GK-player, potentially one strong enough for them to just forfeit.
...Neither party may offer any real-world considerations to persuade the other within the experiment itself. For example, the AI party may not offer to pay the Gatekeeper party $100 after the test if the Gatekeeper frees the AI… nor get someone else to do it, et cetera. The AI may offer the Gatekeeper the moon and the stars on a diamond chain, but the human simulating the AI can’t offer anything to the human simulating the Gatekeeper. No real-world material stakes should be involved except for the handicap (the amount paid by the AI party to the Gatekeeper
Previous thread
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.