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blake8086 comments on A simple game that has no solution - Less Wrong Discussion
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In the Nash equilibrium, what is Player 2's belief if he gets to move? Also, the link you gave is for solving simultaneous move games, and the game I presented is a sequential move game.
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.