5. Suppose that we have the following infinitely repeated Ultimatum game with two players, Ann and Bob. First, Ann makes an offer xA in the interval [0, 1]. Then, Bob sees x and then chooses to Accept or Reject. If an offer xA is accepted, Ann receives 1 xA and Bob receives xA. If an offer is rejected, Bob then gets to make an offer xB. This process is repeated until an offer is accepted, with roles alternating each time. For each time that the game is alternated, Ann discounts at a rate of A while Bob discounts at a rate of B. So if B rejects once, makes an offer and it is accepted, A receives A (1 xB) and B receives B (xB). If there are two rejections and A makes an offer that is accepted, A receives 2 A (1 xA) and B receives 2 B (xA), etc.. (10 points extra credit)

(a) Find the subgame perfect equilibrium