Question 3 (II marks) Consider the following Bayesian game; Player1 can be of type 1' E {4, 6} where Pr(t = 4) = 0.4. Player 1 knows his type, but Player 2 only knows the prior distribution of 1's type. Call 04 Player 1's probability of playing A ifhe is type 4, 0'4 Player 1's probability of playing Aif he is of type 6. and 0'c Player 2's probability of playing C. Player Consider a Bayesian Nash equilibrium in pure strategies where 0'4 E {0, 1}, 0'5 E {0, l}. 0': E {0. 1}. (i) (1 mark) Suppose Player 2 chooses 0': = 0. Player 1's best response is 0'4 =\\:|when r = 4, and 0'5 = E when I = 6. (ii) (0.5 marks) Suppose 0'4 and 0'5 are as in (i). Then Player 2's best response is 0'r = E. (i) (1 mark) Suppose Player 2 chooses 0'E = 1. Player 1's best response is 0'4 =|:|when r = 4, and 0'5 = E when I = 6. (iv) (0.5 marks) Suppose 0'4 and 6.5 are as in (iii). Then Player 2's best response is 0} = E. (v) (1 mark) How many of the following statements are correct? E] - Statement A: There is a BNE in pure strategies where or = l. - Statement E: There is a BNE in pure strategies where 0} = 0. - Statement C: There is a BNE in pure strategies where 0'4 = 0.3 = 0. . Statement D: There are no BNE in pure strategies where 0'4 = 0'5 = 1