Three players select one out of four possible activities. Each player vetos one activity, and the remaining activity is the group's choice. The players make their vetos in sequence with Player 1 making the first veto, Player 2 making the second, and Player 3 making the third. The players' preferences are Player 1: A > D > C > B , Player 2: B > C > A > D , Player 3: C > B > D > A

The preferences are common knowledge among the three players.

(a) Solve the game by backwards induction.