This question deals with two player constant sum games. (a) Consider the following two person zero sum game. Player 2 P Q R S A0434 B 2725 8 612 C D 7903 Player 1 What is the maxmin pure strategy for Player 1 and what payoff can Player 1 guarantee using only pure strategies? (3 marks) (b) In the same game, what is the minmax pure strategy for Player 2 and what payoff can Player 2 guarantee using only pure strategies? (3 marks) (c) In the same game, without doing any further calculations, what can you say about the value of the game when mixed strategies are allowed? (4 marks) (d) Consider now the following two person zero sum game. Player 1 Player 2 A B C D E 85140 B2354 8 Find the optimal (mixed) strategy for Player 1 and the (mixed strategy) value of this game. (6 marks) (e) Without further calculation what can you say about the optimal mixed strat- egy for Player 2? (4 marks)