5. [20 points] Two players, PI and P2, bargain over how to divide the total profit (normalized to 1) between themselves. The game lasts for two periods. A player's utility is u (c) = c, where ce [0, 1] is the amount of profit he obtains. Both players discount utility across periods, where S; E (0, 1) is the discount factor for player i = 1, 2. The timing of the game is as follows. In period 1, first Pl makes an offer (x, 1 - x), where x E [0, 1). That is, P1 gets a and P2 gets 1 - x. In the meantime, P2 also receives an outside offer v E [0, 1]. Then given Pl's offer and the outside offer, P2 decides whether to Page 4 of 4 pages accept either offer or reject both. If P2 accepts any offer, the game ends and the players receive payoffs according to the specific offer. If P2 rejects both offers, the players move on to period 2. In period 2, first P2 makes a counteroffer (y, 1 - y) with y E [0, 1]. In the meantime, PI receives an outside offer u E [0, 1]. Then Pl responds to the offers. If Pl rejects both offers, the game ends and both players receive nothing. Assume that if a player is indifferent between two strategies, he/she will accept the one that is most preferred by his/her opponent. (a) Draw the game tree. Then describe the best responses of both players. (b) Find the subgame perfect equilibrium. Describe the outcome of the game and the payoffs to each player. (c) How does a change with v, u and 62, respectively? Provide intuition