Consider a 4 period alternating offers bargaining game. Specifically, two players, referred to as 1 and 2, have to negotiate on the split a pie of size 1. In period 1, player 1 gets to propose a split of the pie to player 2. If 2 accepts the proposal, then the pie is split between the players as per 1's proposal. If 2 rejects, the interaction continues in the second period with the roles reversed. Now 2, gets to propose a split of the pie. If 1 accepts the proposal, then the pie is split as per 2's proposal. If 1 rejects, then the game proceeds to the third period, with 1 making another proposal. This negotiation process can continue for at most one more period, with 2 having the right to make the proposal in period 4 if agreement is not reached in period 3. If no agreement is reached at the end of period 4, then the game ends with both players getting no share of the pie. Assume, like we did in class, that players care only about their own share of the pie and their utility function is given by u_i(x) = x, for i = 1, 2, where x refers to the share of the pie that i gets. Further, assume that the players discount future periods with the same discount factor . Based on precise calculations, derive the unique SPNE payoff profile of this game?