Question 2 Dad asks Ann and Bob to divide a 9-piece chocolate box according to the following pro- cedure. Ann and Bob each demands a number of chocolate pieces: SA, SB E {0, 1, 2, ,9}. If sa + SB 9, then Ann and Bob are disciplined for being greedy-neither gets any chocolate, dad has it all. (a) Assume first that Ann and Bob have to make their demands simultaneously. Find all pure-strategy Nash equilibria of the game. Is there an equilibrium in which dad eats some chocolate? If yes, identify such an equilibrium; if not, explain why not. (b) Suppose now that dad lets Ann announce her demand sa first, and then Bob gets to choose sb after hearing Ann's demand. How many pure strategies does Bob have in this sequential-move game? (c) Find all pure-strategy subgame perfect equilibria of the extensive-form game de- scribed in part (b). (d) Does the game in part (b) have a Nash equilibrium in which Bob gets 8 pieces of chocolate? Describe each child's strategy in such an equilibrium, or argue why such an equilibrium doesn't exist