Players 1, 2 and 3 bargain over the division of a cake. On the first day, player 1 makes an offer of how to divide the cake among the three of them. Player 2 responds first, either accepting or rejecting. If he accepts, then player 3 responds by either accepting or rejecting. If 3 also accepts, they divide the cake as proposed by player 1 and the game ends. If player 2 rejects or if player 2 accepts and then player 3 rejects,we go to the second day. On the second day, we have only 1/2 of the cake. This time, player 2 makes an offer, 3 responds first, and then, if 3 accepts, 1 responds. As before, if both 3 and 1 accept 2's proposal, they divide the cake and the game ends. If 3 rejects or if 3 accepts but 1 then rejects, we go to the third day. On the third day, we have only 1/4 of the cake. This time, player 3 makes an offer, 1 responds first, and, if 1 accepts, then 2 responds. If the offer is rejected on the third day, then no one gets any cake. Solve the game by backwards induction. (Assume that each player will accept an offer if indifferent between accepting and rejecting.)