Homework 93: {20 points] In a union-management negotiation, the following are the percentages of annual wage increase gainecl by the Union for 1various combinations of union and management strategies: Management M1 M2 M3 U1 1 5 5 U2 2 2 2 Union U3 2 4 4 U4 3 1 2 Determine the best Strategies. and values of the game for the union and management respectively. 9b. For the Rock-Scissors-Paper two- person, zero-sum game, let X1, K2, and X3 be respectively the strategies representing Flock, Scissors, and Paper for the Row Player K and Y1, Y2, and \"f3 be respectively the strategies representing Rock, Scissors, and Paper for the lColumn Player Y. Then the payoff matrix is given below: Column Player Y Y1lRoc k} YEIScisso rs} YlPa per} KllRock} +1 -1 Row Player X Xicissors} -1 0 +1 KBIPaper} +1 -1 D To nd 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'f as well as the fact that the sum of all probabilities adds to 1 as follows: The expected payoff to X if '5" plays Y1 equals the expected payoff to X if Y plays Y2: Dp1-1p2+1p3= 1p1+p2-p3 [equation 1] The expected payoff to X if '1' plays Y1 equals the expected payoff to X if Y plays Y3: Dp1-1p2+1p3=-p1+1p2+p3 [equation 2] All probabilities add to 1: 1p1 +1p2+1p3= 1 [equation 3} [10 points} Use the same solution procedure to find the mixed strategy solution and the expected payoff for 'f 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 '1' Best strategy p1 for X1, Rock q1 for Y1. Rock p2 for K2, Scissors q2 for Y2. Scissors p3 for K3, Paper q3 for Y3, Paper Expected payoff [For full credits, you must recongure the set of 3 linear equations for each player by moving all probabilities to the left side of the equality sign and then solve the 3 reconfigured linear equations through Gaussian elimination or matrix inyersion like you did for Problem 1 in HWD. the Pre-requisite Test}