Question 5 [12 marks) Consider the following game for which we dene the following notation. . 63: Player 1's probability of playing r if type g, . 01,: Player 1's probability of playing r if type b, - 9-,: Player 2's probability of choosing a after observing a choice of r by Player 1, - 5;: Player 2's probability of choosing a after observing a choice of I by Player 1. - Pr(g|r): Player 2's belief that Player1 is type 3 if 1 has played r, - Pr(g|.l): Player 2's belief that Player 1 is type g if 1 has played 1. (7- 4-) (6- 4) (5- 1) (4. 2) (5. 1) (E. 1) (3. 2) (4- 2I! (i) {1 mark) If 65, = 01, = 1. what are consistent beliefs for Player 2? E S Pr(g|r) S E (if there is only one consistent value for Pr(g|r). enter that value into both elds}. (ii) [1 mark) If as = orb = 0, what are consistent beliefs for Player 2? E S Prfg|r) 5 E (if there is only one consistent value for Pr(g|r). enter that value into both elds). (iii) (2 marks) If dz = i and 5b = , what are consistent beliefs for Player 2? E $ Pr(g| r) 5 E (if there is only one consistent value for Pr(g|r), enter that value into both elds) A 2 (iv) (6 marks) There exists at least one PBE in which all player types play pure strategies and in which as = 1. In all these PBE, oh or (v) (2 marks) and beliefs in these PBE are,