Please help me with the problem 5.

The png of problem 1 is the background info.

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\2 Problem 5 Let a profile (N; X; SA, SB; (UA, UB)) be a strategic-form game, where N = {A, B} is the set of players, SA = {1, 2, 3}, SB = {1, 2, 3} are the sets of strategies of players respectively, X = {(aA, aB) | aA E SA, aB E SB} is the set of social alternatives, and uA : SAX SB - R is the payoff function of the player A, which is given by for any aA E SA and any aB E SB, UA (QA, aB) = aA . aB. Likewise, UB : SA X SB - R is the payoff function of the player B, which is given by for any aA E SA and any aB E SB, UB (QA, aB) = aA . aB. (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 can the iterated elimination of weakly dominated strategies reduce the game matrix in order to specify the set of undominated strategies? (4) Is there a Nash equilibrium? If so, specify the set of all Nash equilibria in this game