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GAME THEORY 2017-2018 5 cfu 4 Zero sum games Exercise 47. Consider the zero sum game in extensive form in Figure 1. Write the game in strategic form and solve it. d e f a b c I II -1 0 2 1 5 Figure 1: Exercise 47 Exercise 48. Find if there are equilibria in pure strategies in the following matrices: A =   9 6 11 7 6 8 3 0 6 11 3 2 8 6 12 7 6 7 0 1 10 3 2 6   , B =   3 2 1 0 0 1 2 0 1 0 2 1 3 1 2 2   . Exercise 49. Given the zero sum game described by the following matrix: A =   3 6 5 5 2 4 1 0 3   find a pair of optimal strategies for the players and the value of the game. Exercise 50. Solve the following zero sum game: A =   2 0 2 1 2 3 4 1 2   1 Exercise 51. Given the zero sum game described by the following matrix: A = ( 6 0 5 3 1 5 8 4 ) , find a pair of optimal strategies for the players and the value of the game. Exercise 52. Given the zero sum game described by the following matrix: A =   1 8 4 2 3 5   , find the value of the game and a pair of optimal strategies for the players. Exercise 53. Consider the following zero sum games. How many optimal strategies do the players have? A = ( 1 3 4 2 2 3 ) B = ( 2 3 4 5 3 2 ) C = ( 7 4 3 1 4 5 ) D = ( 5 3 3 3 3 5 ) Exercise 54. Given the zero sum game described by the following matrix: A =   1 5 4 4 6 2   , find the value of the game and a pair of optimal strategies for the players. Exercise 55. Can you apply the indifference principle to solve the following game? X = ( 3 1 4 5 ) Exercise 56. Given the zero sum game: A =   5 a b c 5 d e f 5   , find the values of a, b, c, d, e and f such that a11 and a33 are equilibria. Are there other equilibria in pure strategies? Exercise 57. Given the matrix:   1 2 4 0 3 1 5 a 2   , with a > 0, 2 1. find the conservative values of the game and find a…