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James_Miller comments on A simple game that has no solution - Less Wrong Discussion
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Good thinking, but I picked the payoffs so this approach wouldn't give an easy solution. Consider an equilibrium where Player 1 intends to pick A, but there is a small but equal chance he will pick B or C by mistake. In this equilibrium Player 2 would pick Y if he got to move, but then Player 1 would always intend to Pick C, effectively pretending he had made a mistake.