Show your work when possible. You must justify your results, or you will not get full credit. 1. [9 marks] Consider the following payoff matrices i), ii) and iii). Player 2 ii) Player 2 iin Player 2 Strategy A Strategy B Strategy A Strategy B strategy A Strategy B (2,2) (5,0) (4,3) (3,5) (4,4) (3,5) Player 1 Strategy B Strategy A Player 1 Strategy B Strategy A Strategy B Strategy A Player (0,5) (3,3) (6,2) (2, 1) (3, 5) (2, 7) For each payoff matrix, determine if: a) The payoff matrix is symmetric (Yes or No) b) If Player 1 has a dominant strategy or if Player 2 has a dominant strategy. If so, what are they or state otherwise. c) The game has a Nash Equilibrium? If so what is/are they? You may simply state your answers, no need to show your work. 2. [2 marks] In a 2 x 2 payoff matrix, if both players have a dominant strategy, but they do not have the same dominant strategy (say Player 1 has dominant strategy A while Player 2 has dominant strategy B), then can that payoff matrix ever be symmetric? Explain. Use an example in your explanation if possible. Page 1 of 4NATS1595, Assignment 3 Due : March 12 by 11:59am 3. [2 marks] Fill in the following payoff matrix so that there is NO pure strategy Nash Equilibrium. You can not use any example from this assignment. Player 2 Strategy A Strategy B T o a 3 & ( 5 ' 7 ) ( 6) 4 ) & a a) What is the mixed strategy Nash equilibrium. Suppose Player 1 plays strategy A with probability g, and Player 2 plays strategy A with probability p. b) Calculate the expected payofl for each player at the mixed strategy Nash equilibrium