Consider the following four period alternating offer bargaining game (players are dividing a dollar), with different discount factors , and 82 for the two players. player 1 proposes the division (w, 1 - w) in period 1 where any we [0, 1] is possible (so w represents player l's proposed share of the dollar). player 2 can accept or reject. if player 2 accepts then the game ends with payoffs (w, 1-w). if player 2 rejects, then she proposes (1 - x, x) in period 2 where any xe [0, 1] is possible. player i can accept or reject. if player 1 accepts the game ends with payofl's (8,(1 - x), 02x). if player 1 rejects, then she proposes (y, 1-y) in period 3 where any ye [0, 1] is possible. player 2 can accept or reject. if player 2 accepts the game ends with payoffs (8y, 8(1 - if player 2 rejects, then she proposes (1-2, z) in period 4 where any ze [0, 1] is possible. player 1 can accept or reject. if player 1 accepts the game ends with payoffs (& (1-2), 822). if player 1 rejects the game ends with payoffs (0,0). (a) in the unique subgame perfect nash equilibrium, what is player l's demand w (as a function of , and 82)? (b) why must player 2 accept the demand you found in part (a) spne even though she is indiffer- ent between accepting and rejecting it? (c) suppose that 8, = 8) = 8. does player 1 benefit from making the first demand (i. e. is w 0.5? ) when d = 0.5? does player 1 benefit from making the first demand when : = 0.9? for what level of 8 is player 1 indifferent between making the first demand (i. e. when is w = 0. suppose now that 8 # 82 and there is 20 period alternating offer game with player 1 making offers in odd periods and player 2 making offers in even periods. (d) suppose that 82 = 0.97. does player l's demand more or less than half the dollar in period 1? (hint: although i haven't told you dı, you don't need this, because you don't need to solve for the exact solution. think about player 2's continuation payoff is in period (e) suppose that 82 < 0.5 does player l's demand more or less than half the dollar in period 1?