Game Theory [15 marks total] 4.1 [8 marks] We call a number low if it belongs to the set {1, 2}. We call it high if it belongs to the set {3,4}. Consider the following matrix game. Player C chooses a number from {1,2,3,4} and player R simultaneously chooses either "high" or "low". If player R guesses correctly what set player C picked from, then player C must pay Ex to player R, where x is the number that player C picked. If player R guesses incorrectly, then that amount must be paid from player R to player C. Determine the payoff matrix. Then write down the linear program to determine the optimal randomized strategy for player C. Do not solve the linear program! Game Theory [15 marks total] 4.1 [8 marks] We call a number low if it belongs to the set {1, 2}. We call it high if it belongs to the set {3,4}. Consider the following matrix game. Player C chooses a number from {1,2,3,4} and player R simultaneously chooses either "high" or "low". If player R guesses correctly what set player C picked from, then player C must pay Ex to player R, where x is the number that player C picked. If player R guesses incorrectly, then that amount must be paid from player R to player C. Determine the payoff matrix. Then write down the linear program to determine the optimal randomized strategy for player C. Do not solve the linear program