(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.

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 : SAX 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