1. Two players have to split a dollar. There are two periods. In the first period, player 1 makes an offer on how to divide the dollar; then player 2 decides whether to accept or reject the offer; if player 2 accepts the offer, they split the dollar as accorded, and the game ends; if player 2 rejects the offer, then they move to the second period. In the second period, player 2 gets to make an offer on how to split the dollar; if player 1 accepts, they split the dollar as accorded; if player 1 rejects the offer, nobody receives any share of the dollar, and the game ends. Assume both players have a discount factor of . Assume also that when indifferent, a player accepts the proposal.

a) Draw the game tree.

(b) Find the SPNE.