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James_Miller comments on A simple game that has no solution - Less Wrong Discussion
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Please answer the question, what would you do if you are player 2 and get to move? Might you pick Y? And if so, how can you conclude that Player 1 was irrational to not pick A?
I will realize that I was lied to, and the player 1 is not rational. Now, if you are asking what player 2 should do in a situation where Player 1 does not follow the best possible strategy, I think Eliezer's solution above works in this case. Or Emile's. It depends on how you model irrationality.
I don't agree since you can't prove that not picking A is irrational until you tell me what player 2 would do if he gets to move and we can't answer this last question.