Why is that the caseExplain with more details please

Two people select a policy that affects them both from three feasible policy choices X, Y and Z. They do so by alternately vetoing policies until only one remains, according to the following procedure: First, person 1 vetoes one of the three policies. If more than one policy remains, person 2 then vetoes a policy. If more than one policy still remains, person 1 then vetoes another policy. The process continues until a single policy remains unvetoed, which is then implemented. Suppose that both persons have transitive preferences, and that person 1 prefers X to Y to Z, and 2 prefers Z to Y to X. The resulting sequential game ends after rounds. (One "round" in this question should be interpreted as one of the players making a veto. So if the game ends after player A vetoes a policy, then player B vetoes a policy, and finally player A vetoes another policy, that would be 3 rounds.) The unique backward induction equilibrium of the game consists of person 1 vetoing Z and person 2 vetoing X. x person 1 vetoing Z, person 2 vetoing Y after 1 vetoes X, person 2 vetoing X after 1 vetoes Y, and person 2 vetoing X after 1 vetoes Z. none of the other provided answers are correct. person 1 vetoing Y and person 2 vetoing X. person 1 vetoing Y, person 2 vetoing Y after 1 vetoes X, person 2 vetoing X after 1 vetoes Y, and person 2 vetoing X after 1 vetoes Z. Mark 0.00 out of 2.00 The correct answer is: person 1 vetoing Z, person 2 vetoing Y after 1 vetoes X, person 2 vetoing X after 1 vetoes Y, and person 2 vetoing X after 1 vetoes Z. The implemented policy is . Z.X Mark 0.00 out of 1.00 The correct answer is: Y. The critical thing to note here is that a strategy for person 2 must specify what person 2 does after observing any possible initial veto of person 1--otherwise, there will be no basis on which to decide what player 1 should do at the start of the game. Make sure to sketch a corresponding game tree