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LimberLarry comments on A simple game that has no solution - Less Wrong Discussion

10 Post author: James_Miller 20 July 2014 06:36PM

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Comment author: LimberLarry 23 July 2014 05:11:49AM 0 points [-]

You seem to be treating the sub-problem, "what would Player 2 believe if he got a move" as if it is separate from and uninformed by Player 1's original choice. Assuming Player 1 is a utility-maximizer and Player 2 knows this, Player 2 immediately knows that if he gets a move, then Player 1 believed he could get greater utility from either option B or C than he could get from option A. As option B can never offer greater utility than option A, a rational Player 1 could never have selected it in preference to A. But of course that only leaves C as a possibility for Player 1 to have selected and Player 2 will select X and deny any utility to Player 1. So neither option B nor C can ever produce more utility than option A if both players are rational.