3. (Altruism in the Prisoners' Dilemma) Assume that the two players have the same choices as...

 

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3. (Altruism in the Prisoners' Dilemma) Assume that the two players have the same choices as in the standard Prisoners' Dilemma, namely, confess (C) and deny (D). For simplicity, however, assume that each pair of action choices results in the players receiving a sum of money equal to the numbers in the cell corresponding to that action profile in the following bimatrix: C D C 1,1 3.0 D 0,3 2.2 Thus, if player 1 chooses C and player 2 chooses D, player 1 gets $3 and player 2 gets nothing. Now, assume that each player has a certain degree of altruism in that she cares about the money received by the other player in addition to what she receives herself. Specifically, assume that the payoff function of player 1 is given by u(a,a)=m(aa)+m(aa), where is the action chosen by player 1, a2 is the action chosen by player 2, m (a, a) is the money received by player 1 when he chooses the action a, and player 2 chooses a, m(a, a) is the money received by player 2 in the same circumstance, and a is a constant such that 0 3. (Altruism in the Prisoners' Dilemma) Assume that the two players have the same choices as in the standard Prisoners' Dilemma, namely, confess (C) and deny (D). For simplicity, however, assume that each pair of action choices results in the players receiving a sum of money equal to the numbers in the cell corresponding to that action profile in the following bimatrix: C D C 1,1 3.0 D 0,3 2.2 Thus, if player 1 chooses C and player 2 chooses D, player 1 gets $3 and player 2 gets nothing. Now, assume that each player has a certain degree of altruism in that she cares about the money received by the other player in addition to what she receives herself. Specifically, assume that the payoff function of player 1 is given by u(a,a)=m(aa)+m(aa), where is the action chosen by player 1, a2 is the action chosen by player 2, m (a, a) is the money received by player 1 when he chooses the action a, and player 2 chooses a, m(a, a) is the money received by player 2 in the same circumstance, and a is a constant such that 0