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GAME THEORY 2017-2018 5 cfu 3 Games in strategic form and Nash equilibria Exercise 33. Find the values of (a, b) such that the following game has an outcome determined by elimination of strictly dominated strategies.   (3, 3) ( a, b) (4 , 2) (2, 2) (6 , 3) (3 , 1) (5, 4) (7 , 8) (6 , 1)   Exercise 34. Find the equilibria in pure strategies of the following game   (5, 4) (1 , 6) (0 , 3) (5 , 1) (5, 3) (3 , 2) (1 , 0) (4 , 3) (2, 5) (4 , 0) (1 , 5) (2 , 1)   Exercise 35. Consider the following game in strategic form: ( (1, 2) (1 , 3) (0, 2) ( a, b) ) Find the Nash equilibria in pure strategies for different values of a and b. What are the conditions on a and b for the game to be derived from a game in extensive form with perfect information? Exercise 36. Find the Nash equilibria for the Battle of Sexes. Exercise 37. Find the equilibria in pure and mixed strategies of the following game ( (3, 3) ( −1,−3) (3,−1) (1 , 1) ) Exercise 38. Given the bimatrix: ( (1, 1) (1 , 1) (0, 1) (2 , 2) ) , apply the indifference principle to find Nash equilibria. Do the same by drawing the best reaction multifiunctions and compare the results. 1 Exercise 39. Find the Nash equilibria of the following game ( (5, 5) (0 , 5) (5, 0) (1 , 1) ) Exercise 40. Consider the game in extensive form in Figure 1. Apply backward induction to solve the game. Then, write the game in strategic form and find the Nash equilibria. I II (2, 0) A B C (3, 2) D (1, 2) Figure 1: Exercise 40 Exercise 41. Given the bimatrix game: A = ( (3, 2) (0 , 1) (2, 3) (2 , 3) ) , find the pure Nash equilibria of the game. Then, find a game in extensive form with perfect information such that A represent its strategic form and solve the game by using backward induction. Compare the results. Exercise 42. Consider the following…