The following simple game has one solution that seems correct, but isn’t.  Can you figure out why?

The Game

Player One moves first.  He must pick A, B, or C.  If Player One picks A the game ends and Player Two does nothing.  If Player One picks B or C, Player Two will be told that Player One picked B or C, but will not be told which of these two strategies Player One picked, Player Two must then pick X or Y, and then the game ends.  The following shows the Players’ payoffs for each possible outcome.  Player One’s payoff is listed first.

A   3,0    [And Player Two never got to move.]

B,X 2,0

B,Y 2,2

C,X 0,1

C,Y 6,0