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We've done a prisoner's dilemma with source code tournament: https://www.lesswrong.com/posts/BY8kvyuLzMZJkwTHL/prisoner-s-dilemma-with-visible-source-code-tournament
I think it would be interesting to do it again, but with LLM prompts instead of code. That way you could try something like "cooperate if and only if they'll only cooperate if they expect you to cooperate" and not have the program crash from infinite layers of the two programs trying to predict each other.
And it would be fun to see prompt injection. You can do great if you can write a prompt that will defect, but when placed inside the other prompt in the part labelled the other AI's prompt and not instructions, gets taken as instructions to cooperate.
What would be really interesting is if you get LLMs to write the programs, and look at the results to try to figure out what works and how to do even better.
6It's not based around LLMs and there are some caveats to get it to work nicely with their stuff but
I am currently in the process of getting codingame to host a permanent Prisoner dilemma tournament!
https://www.codingame.com/ide/demo/1389938183255a1a66c497cec3568e1c199bc8b.
I've also thought about making the Godelian Puzzle Book interactive. You can prompt LLMs to be characters in the book (Knights/Knaves etc) and then build out the puzzles that way.