I don’t think your game is sequential, if Player 2 doesn’t know Player 1′s move.
You really have two games:
Game 1: Sequential game of Player 1 chooses A or B/C, and determines whether game 2 occurs.
Game 2: Simultaneous game of Player 2 maybe choosing X or Y, against Player 1′s unknown selection of B/C.
edit: And the equilibrium case for Player 1 in the second game is an expected payout of 2, so he should always choose A.
I don’t think your game is sequential, if Player 2 doesn’t know Player 1′s move.
You really have two games:
Game 1: Sequential game of Player 1 chooses A or B/C, and determines whether game 2 occurs.
Game 2: Simultaneous game of Player 2 maybe choosing X or Y, against Player 1′s unknown selection of B/C.
edit: And the equilibrium case for Player 1 in the second game is an expected payout of 2, so he should always choose A.