Problem 3 - Bargaining Model with Finite Horizon Let's consider Rubinstein's bargaining model as discussed in class, but with a finite time horizon. A time period is indexed by t = n,..., 1, where period [1 is the starting period and period 1 is the final period. Player 1 makes an offer in every odd period, and player 2 makes an offer in every even period. Let (x', 1- x*) denote an offer made in period t which gives it to player 1 and l-x' to player 2. If they cannot agree even in period 1, both of get payoffs of 0. If they agree to a division of (X,1- x) in period t, the payoffs of players 1 and 2 are 8"-" x and 6"-'(1 9 K), respectively. (Note 81, 8, can in principle be different). In all of the following questions, restrict attention to subgame-perfect Nash equilibrium. (a) In period 1, what offer does player 2 accept? What offer does player 1 make to player 2, and does player 2 accept this offer? What are their payoffs? (b) In period 2, what offer does player 1 accept? What offer does player 2 make to player, and does player I accept this offer? What are their payoffs? (Use the information you got from part (a)). (c) Suppose both players anticipate that they will agree to a division of (x-1,1-x-1) in period t-1 if they cannot agree at period t, where t is odd. What offers does player 2 accept in period I? What offer does player 1 make to player 2, and does player 2 accept this offer? What are their payoffs? Do the same exercise when t is even. (d) What is the outcome of the backward induction when n is odd and when n is even? What happens with the equilibrium when