I was making the more general point that impossible situations (abstract arguments that aren’t modeled by any of the “possible” situations being considered) can matter, that impossibility is not necessarily significant. Apart from that, I agree that we don’t actually have a good argument for impossibility of any given action by Player 1, if it depends on what Player 2 could be thinking.
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.
But why is not picking A “impossible-in-reality”? You can not answer until you tell me what Player 2′s beliefs would be if A was not picked.
I was making the more general point that impossible situations (abstract arguments that aren’t modeled by any of the “possible” situations being considered) can matter, that impossibility is not necessarily significant. Apart from that, I agree that we don’t actually have a good argument for impossibility of any given action by Player 1, if it depends on what Player 2 could be thinking.
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.