Question 1 (30 points): Consider the following Prisoners' Dilemma D C D 3.3 9,1 C 1,9 6.6 Suppose the above stage game is played infinitely. Each player has a discount factor 6 E (0, 1).a) (10 points) Consider any history in which the outcome in the last period is (C,D). Under what conditions on 6 6 (0, 1), if any, is following the strategy below optimal? You need to check the one-shot deviation property when last period outcome is (C,D). Choose C after any history in which the outcome in the last period is either (D,C) or (C,C). Choose D after any history in which the outcome in the last period is either (D.D) or (C,D).b) (10 points) Consider any history in which the outcome in the last period is (D,D). Under what conditions on 6 6 (0, 1), if any, is following the strategy below optimal? You need to check the one-shot deviation property when last period outcome is (D,D). Choose C after any history in which the outcome in the last period is either (D,C) or (C,C). Choose D after any history in which the outcome in the last period is either (D,D) or (C,D).C) (10 points) Consider any history in which the outcome in the last period is (C,C). Under what conditions on & E (0, 1), if any, is following the strategy below optimal? You need to check the one-shot deviation property when last period outcome is (C,C). Choose C after any history in which the outcome in the last period is either (D,C) or (C,C). Choose D after any history in which the outcome in the last period is either (D.D) or (C,D)