Consider the following bargaining problem: 20 dollars needs to be split between Alice and Bob.

Stage 1: Bob makes an initial offffer (between $0 and $20). Alice then responds by either

(1) accepting Bob's initial offffer and ending the game, or (2) rejecting and moving the game to stage 2.

Stage 2: Alice makes a counter offffer (between $0 and $20). Bob then respond by either

(1) accepting Alice's counter offffer and ending the game, or (2) rejecting and moving the game to stage 3.

Stage 3: Bob makes a fifinal offffer (between $0 and $20). Alice then responds by accepting or rejecting Bob's fifinal offffer.

If Alice rejects, both Alice and Bob get nothing and the game ends.

If Alice accepts, the money is split per the fifinal offffer and the game ends.

Alice discounts the future by 10%. That is, from the point view of the current stage, one dollar received in the next stage is worth 0.9 dollar to Alice. Bob discounts the future by 20%. That is, from the point view of the current stage, one dollar received in the next stage is worth 0.8 dollar to Bob.

Assume that when a player is indifffferent between accepting and rejecting an offffer, he or she will choose to accept the offffer. Calculate the subgame perfect Nash equilibrium of this bargaining problem.