LimberLarry comments on A simple game that has no solution - Less Wrong Discussion
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Because for Player 1 to increase his payoff over picking A, the only option he can choose is C, based on an accurate prediction via some process of reasoning that player 2 will pick X, thereby making a false prediction about Player 1's behaviour. You have stated both players are rational, so I will assume they have equal powers of reason, in which case if it is possible for Player 2 to make a false prediction based on their powers of reason then Player 1 must be equally capable of making a wrong prediction, meaning that Player 1 should avoid the uncertainty and always go for the guaranteed payoff.
To formulate this mathematically you would need to determine the probability of making a false prediction and factor that into the odds, which I regret is beyond my ability.