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LimberLarry comments on A simple game that has no solution - Less Wrong
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But this does not make sense because then player 1 will know that player 2 will play X, so Player 1 would have been better off playing A or B over C.
Exactly, but B is never a preferable option over A, so the only rational option is for Player 1 to have chosen A in the first place, so any circumstance in which Player 2 has a move necessitates an irrational Player 1. The probability of Player 1 ever selecting B to maximize utility is always 0.