Consider the following 2-player zero-sum game. Each player separately chooses a number from the set {1, 2, 3}. Both players then reveal their numbers. If the numbers match, the row player must pay £3 to the column player, otherwise, the player with the lower number must pay £1 to the player with the higher number.
(i) Give the payoff matrix for this game from the perspective of the row player. Also give the security level for each of the player’s strategies.
(ii) Does this game have a pure Nash equilibrium? If so, give all pure Nash equilibria for the game. If not, explain why.
(iii) Formulate a linear program that finds the row player’s best mixed strategy in this game (you do not need to solve this program).
