Here’s another perspective. Suppose that now Bob and Carol have symmetrical roles: each one asks a question, allows Alice to answer, and then reveals the right answer. Alice gets a reward when ey answer correctly. We can now see that perfect honesty actually is tractable. It corresponds to an incomplete hypothesis. If Alice learns this hypothesis, ey answer correctly any question ey already heard before (no matter who asks now and who asked before). We can also consider a different incomplete hypothesis that allows real-time simulation of Carol. If Alice learns this hypothesis, ey answer correctly any question asked by Carol. However, the conjunction of both hypotheses is already intractable. There’s no impediment for Alice to learn both hypotheses: ey can both memorize previous answers and answer all questions by Carol. But, this doesn’t automatically imply learning the conjunction.
Here’s another perspective. Suppose that now Bob and Carol have symmetrical roles: each one asks a question, allows Alice to answer, and then reveals the right answer. Alice gets a reward when ey answer correctly. We can now see that perfect honesty actually is tractable. It corresponds to an incomplete hypothesis. If Alice learns this hypothesis, ey answer correctly any question ey already heard before (no matter who asks now and who asked before). We can also consider a different incomplete hypothesis that allows real-time simulation of Carol. If Alice learns this hypothesis, ey answer correctly any question asked by Carol. However, the conjunction of both hypotheses is already intractable. There’s no impediment for Alice to learn both hypotheses: ey can both memorize previous answers and answer all questions by Carol. But, this doesn’t automatically imply learning the conjunction.
It’s absurd (in a good way) how much you are getting out of incomplete hypotheses. :)