Question 3 (25 points) (Altruistic players in the Prisoners' Dilemma) Each of two players has two possible actions, cooperate (C) and defect (D). The monetary payoff to each action profile are given in the following table However, the above table does not represent the true preferences of the players, as they care about what the other player earns as well as their own earnings. In particular, if m,(a) is the amount of money earned by player i and mJ-(a) is the amount of money earned by player j; then the payoff to player i is m,-(a) + amj(a) ; where a 2 0. Of course, when a = 0; the payoffs coincide with the ones in the above table. For example, player 1's payoff to action profile (C,C) is u1(C;C) = 10 + 104x and player 1's payoff to action profile (CD) is u1(C; D) 2 2+ 151