In a classical game all the players move simultaneously.
I’m not sure what you mean by “classical game” but my game is not a simultaneous move game. Many sequential move games do not have equivalent simultaneous move versions.
“I hope you agree that the fact that player 2 gets to make a (useless) move in the case that player 1 chooses A doesn’t change the fundamentals of the game.”
I do not agree. Consider these payoffs for the same game:
A 3,0 [And Player Two never got to move.]
B,X 2,10000
B,Y 2,2
C,X 0,1
C,Y 4,4
Now although Player 1 will never pick A, its existence is really important to the outcome by convincing Player 2 that if he moves C has been played.
I do not agree. Consider these payoffs for the same game: …
Different payoffs imply a different game. But even in this different game, the simultaneous move version would be equivalent. With regards to choosing between X and Y, the existence of choice A still doesn’t matter, because if player 1 chose A X and Y have the same payoff. The only difference is how much player 2 knows about what player 1 did, and therefore how much player 2 knows about the payoff he can expect. But that doesn’t affect his strategy or the payoff that he gets in the end.
I’m not sure what you mean by “classical game” but my game is not a simultaneous move game. Many sequential move games do not have equivalent simultaneous move versions.
“I hope you agree that the fact that player 2 gets to make a (useless) move in the case that player 1 chooses A doesn’t change the fundamentals of the game.”
I do not agree. Consider these payoffs for the same game:
A 3,0 [And Player Two never got to move.]
B,X 2,10000
B,Y 2,2
C,X 0,1
C,Y 4,4
Now although Player 1 will never pick A, its existence is really important to the outcome by convincing Player 2 that if he moves C has been played.
Different payoffs imply a different game. But even in this different game, the simultaneous move version would be equivalent. With regards to choosing between X and Y, the existence of choice A still doesn’t matter, because if player 1 chose A X and Y have the same payoff. The only difference is how much player 2 knows about what player 1 did, and therefore how much player 2 knows about the payoff he can expect. But that doesn’t affect his strategy or the payoff that he gets in the end.