Only want the solution of problem 3

1 Problem 1 Two criminals have been caught by the police. Because of lack of evidence the prosecution needs a confession to convict. If no confession ensures, they will be charged and convinced for a minor offense earning them one year less than a conviction for the main crime. The prosecutor offers each prisoner the following deal. If she confesses, and the other does not, she will get three years off her sentence whereas the other prisoner will get an extra year in prison. If both confess, they will be punished according to the law (no reductions). This story easily translates into the following strategic form game (N; X; SA, 83; (uA, 253)) with N E {A, B} is the set of players; S A E {0, N} E S B is the set of strategies common to both players, where C implies \"confess\U1(T,L) : 1;u1(T,R)=0;u1(B,L)=1,u1(B,R):0; 11.2 (T,L) = 1; U2 (T,R) = 1; 11,2 (3,11) = 0; 11.2 (B,R) = 0. (1) Draw the game matrix of this game. (2) Is there a strictly dominant strategy equilibrium of this game? If so, write down all of strictly dominant strategy equilibria in this game. If no, write down the reason why no strictly dominant strategy equilibrium exists. (3) Is there a weakly strictly dominant strategy equilibrium of this game? If so, write down all of weakly strictly dominant strategy equilibria in this game. If no, write down the reason why no weakly dominant strategy equilibrium exists. 3 Problem 3 Consider a two-player game (N; X; SA, SB; (UA, UB)), where N = {A, B} is the set of players, SA = {S'A, S'A, S'A}, SB = {SB, SB, SB, SB) are the sets of strategies of players respectively, and uA : SA X SB - R is the payoff function of the player A, which is given by UA (SA, SB) = 4; UA (SA, SB) = 3; UA (SA, SB) = 1; UA (SA, SB) = 7; UA (SA, SB) = 3; UA (S'A, SB) = 2; UA (S'A, SB) = 0; UA (S'A, SB) = 5; UA (SA, SB) = 4; UA (SA, SB) = 4; UA (SA, SB) = 0; UA (SA, SB) = 5, while uB : SAX SB - R is the payoff function of the player B, which is given by UB (SA, SB) = 2; UB (SA, SB) = 3; UB (SA, SB) = 2; UB (SA, SB) = 2; UB SA, SB) = 8; UB (SA, SB) = 4; UB (S'A, SB) = 2; UB (SA, SB) = 5; UB SA, SB) = 1; UB (SA, SB) = 2; UB (SA, SB) = 1; UB (SA, SB) = 0. (1) Draw the game matrix of this game. (2) Is there a weakly strictly dominant strategy equilibrium of this game? If so, write down all of weakly strictly dominant strategy equilibria in this game. If no, write down the reason why no weakly dominant strategy equilibrium exists. (3) If the answer of the question (2) is no, then apply the iterated elimina tion of weakly dominated strategies and describe the procedure to reduce the game matrix from the original one. Moreover, specify the set of undominated strategies