Your behavior in impossible-in-reality but in some sense possible-to-think-about situations may well influence others’ decisions, so it may be useful to decide what to do in impossible situations if you expect to be dealing with others who are moved by such considerations. Since decisions make their alternatives impossible, but are based on evaluation of those alternatives, considering situations that eventually turn out to be impossible (as a result of being decided to become impossible) is a very natural thing to do.
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.
Your behavior in impossible-in-reality but in some sense possible-to-think-about situations may well influence others’ decisions, so it may be useful to decide what to do in impossible situations if you expect to be dealing with others who are moved by such considerations. Since decisions make their alternatives impossible, but are based on evaluation of those alternatives, considering situations that eventually turn out to be impossible (as a result of being decided to become impossible) is a very natural thing to do.
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.