1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors. Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: "paper covers rock: if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper: if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 3 by the other player. "rock breaks scissors: if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper scissors rock 0 -3 1 paper 1 0 -1 scissors -1 3 0 3 (a) Show that XT= (}, }, }) and y (}; ; ) together are not a Nash equilibrium for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy XE A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x A(R) that has an optimal security level for Rosemary and a mixed strategy y A(C) that has an optimal security level for Colin