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