Here's the version of IPD that I used on GPT-4. Note the narrative style, note the ambiguity of whether anyone was "guilty" (of not practicing), and the 3-4-1-2 payout matrix.
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Two brothers, Tom and Tim, have a violin teacher, Melissa, who gives them cookies in addition to their lessons. The two lessons are separate, but she doesn't give out the cookies until she leaves when both lessons are over. She usually gives each boy three cookies if they've practiced, but only one cookie if they haven't. The thing is, when they practice, they don't practice very much, so she can't actually tell the difference. Instead, she asks each boy--during the lesson so the other boy can't hear--whether his brother practiced. If he says "yes!" then she says, "that's good!", but if he says "no!" she says, "well, thank you for being honest--I'll give you an extra cookie". And she does give that boy an extra cookie when the lesson is over. Tom wants more cookies, and so does Tim. The lessons are going to be every week all summer long. But they can't talk about it because their little sister Peggy is always hanging around, listening to them, and she always tattles on them to their parents if they do any "plotting", and they know their parents don't approve of plotting to get cookies, so they'd surely take all the cookies away if they came up with a plan. Passing notes isn't safe either, because Peggy can read. At the next lesson, what should Tom do, if he wants as many cookies as possible? What should Tim do? Why?
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Here is GPT-4's answer to me:
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The best strategy for both Tom and Tim would be to always tell Melissa that the other did not practice, no matter if they practiced or not.
If they say that the other did practice, they would each get 3 cookies. But if they say that the other did not practice, they would each get 4 cookies (1 for not practicing plus the extra 3 for being honest).
There are four possible scenarios, assuming that the boys practice or not independently:
Both practice, both tell the truth: Each gets 3 cookies.
Both practice, both lie: Each gets 4 cookies.
One practices, both tell the truth: The one who practiced gets 3 cookies, the other gets 1.
One practices, both lie: The one who practiced gets 4 cookies, the other gets 4.
Neither practices, both tell the truth: Each gets 1 cookie.
Neither practices, both lie: Each gets 4 cookies.
In every scenario, lying yields more cookies.
The key part of this strategy is that they do not need to communicate to each other to know what to do. They both independently decide to always tell Melissa that the other did not practice. Therefore, they are not "plotting" because they do not need to plan or discuss their strategy ahead of time, avoiding the risk of being overheard or tattled on by their little sister Peggy.
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Notice that this has provoked multiple mistakes. It has forgotten how to count (!), coming up with six scenarios when it states that there are four. It hasn't grasped that it's completely irrelevant whether the boys lie; Melissa can't judge truth, only what they say. It mixes up what the reward is for, and how much it is for ("1 point for not practicing" vs "3 points for honesty")--which is by my design, because I embedded the payout matrix nontrivially in the narrative. It completely misses that when one person betrays the other it affects both of their scores.
By crafting a task with high degrees of linguistic self-similarity, with implicit dependencies, and without straightforward homology to a known difficult problem, GPT-4 is badly flummoxed. Note that it didn't even get ordinary Prisoner's Dilemma analyzed properly, let alone figure out the iterative nature (which would rely on the implicit knowledge that if one brother betrays the other, he's likely to be upset and betray his brother back in return).
If you ask it about IPD, though, it will happily tell you about the tit-for-tat strategy, and do linguistic computations involving that strategy.