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4. (10 points) Consider the twoplayer bargaining game discussed in class in which the two players make alternating offers of splitting one unit of a perfectly divisible good. In round 1, player 1 offers a division (113,1 2:) that player 2 can accept or reject; if player 2 rejects, then in round 2, player 2 offers (y, 1 y) that player 1 can accept or reject; etc. In lecture we discussed a model where the payoff functions of the players are identical, that is, u1(3) 2 152(3) = s for any 3 E [0, 1]. We shall explore an alternative model where the payoff functions to the players are different. Specically, suppose player 1's payoff function is v1(x) = 1 (1 a:)2 and player 2's payoff function is 11201:) = 2:. Analyze the innite horizon alternating offers bargaining game where the players have a common discount factor (5, but the payoff functions are different for different players. If you are having trouble with the innite horizon version, analyze a three round game where the exogeneous settlement in the third round (if player 2 rejects 1's offer a second time) is (s, 1 8). You should nd a subgame perfect Nash equilibrium strategy for each player. Note that your strategy should fully speciy what each player does at each round in which they are asked to play