Consider the following Bayesian game. Player 1 can be of type t E {4, 6} where Pr(t : 4) : 0.5. 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 if he is type 4, (76 Player 1's probability of playing A if he is of type 6, and an, Player 2's probability of playing C. Player 2 A 015 1,0 Player 3 1,0 0,2 Consider a Bayesian Nash equilibrium in pure strategies where 0'4 E {0, 1}, 0'5 6 {0, 1},ac E {0, 1}. (i) (1 mark) Suppose Player 2 chooses arc : 0. Player 1's best response is 04 : E when t : 4, and 0'5 : Ewhen t : 6. (ii) (0.5 marks) Suppose a4 and 05 are as in (i). Then Player 2's best response is cr,g : E. (i) (1 mark) Suppose Player 2 chooses arc : 1. Player 1's best response is 04 : E when t : 4, and 05 : Ewhen t : 6. (iv) (0.5 marks) Suppose a4 and 06 are as in (iii). Then Player 2's best response is are : E. (v) (1 mark) How many of the following statements are correct? a Statement A: There is a BNE in pure strategies where are : 1. - Statement B: There is a BNE in pure strategies where (7,, : 0. - Statement C: There is a BNE in pure strategies where 04 : 0'5 : 0. - Statement D: There are no BNE in pure strategies where 0'4 : (76 : 1. Make sure you round your answers to 3 decimal places if necessary