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 | D c D 55 15,2 c 2,15 10,10 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 mi(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 mi(a) + rxmj(a) ; where a 2 0. Of course, when a 2 0; the payoffs coincide with the ones in the above table. For example, player 1's payoff to action prole (C,C) is u1(C;C) = 10 + 1001 and player 1's payoff to action prole (C,D) is u1(C; D) : 2+ 1504 (a) (5 points) Write down the strategic form of this game for a = 1: Is this game a Prisoners' Dilemma game? (b) (10 points) Find the range of values of at for which the resulting game is the Prisoners' Dilemma. For values of ac for which the game is not the Prisoners' Dilemma, find its Nash equibria