9b. For the Rock-Scissors-Paper two-person, zero-sum game, let X1, X2, and X3 be respectively the strategies representing Rock, Scissors, and Paper for the Row Player X and Y1, Y2, and Y3 be respectively the strategies representing Rock, Scissors, and Paper for the Column Player Y. Then the payoff matrix is given below: Column Player Y Y1(Rock) Y2(Scissors) Y3(Paper) X1(Rock) 0 +1 -1 Row Player X X2(Scissors) -1 0 +1 X3(Paper) +1 - 1 To find the mixed strategy solution for this game based on Nash Equilibrium, the solution procedure is to assign probabilities p1, p2, and p3 respectively to X1, X2, and X3, then set up 3 linear equations for the 3 probabilities by equalizing the expected payoffs to X for different strategies of Y as well as the fact that the sum of all probabilities adds to 1 as follows: The expected payoff to X if Y plays Y1 equals the expected payoff to X if Y plays Y2: Op1-1p2+1p3= 1p1+0p2-p3 (equation 1) The expected payoff to X if Y plays Y1 equals the expected payoff to X if Y plays Y3: Op1-1p2+1p3=-p1+1p2+0p3 (equation 2) All probabilities add to 1: 1p1 +1p2+1p3= 1 (equation 3) (10 points) Use the 3 equations to solve the probabilities and thus the mixed strategy solution and the expected payoff for X. (10 points) Use the same solution procedure to find the mixed strategy solution and the expected payoff for Y and summarize the overall solution for this game with the values of all the probabilities and the expected payoffs for the players shown below: Player X Y Best strategy p1 for X1, Rock q1 for Y1, Rock p2 for X2, Scissors q2 for Y2, Scissors p3 for X3, Paper q3 for Y3, Paper