Ashok (A) and Beatrice (B) are a two-member team in an IT firm. Ashok decides first whether to work on difficult problems (D) or easy problems (E). Subsequently, Ashok and Beatrice choose their own effort levels. We assume that the effort choices are made separately but simultaneously. Let XA and XB denote the level of effort exerted by Ashok and Beatrice respectively. Both XA and Xx can take only two values: 4 or 10. That is Xi E (4, 10} for i = A, B. If Ashok chooses E Ashok gets max {XA, XB} - 0.5XA Beatrice gets max {XA, XB} - 0.5XB where "max" denotes maximum, e.g., max {2,3} = 3. If Ashok chooses D Ashok gets min {4XA, 4XB) - XA . Beatrice gets min (4XA, 4XB) - XB where "min" denotes minimum, e.g., min (2,3) = 2. (i) (1.5 marks) Suppose Ashok chooses E. Consider the subgame associated with that choice (i.e. the one that arises following E). Write the corresponding payoff matrix. . Identify all pure strategy Nash equilibria. . Derive the Nash equilibrium in mixed strategies. (ii) (1.5 marks) Suppose Ashok chooses D. Consider the subgame associated with that choice (i.e. the one that arises following D) and answer the three questions stated in part (i). (iii) (3 marks) Now consider the entire game . Identify a pure strategy profile that is a Subgame Perfect Nash equilibrium (SPNE). Explain why it is SPNE Identify a pure strategy profile that is a Nash equilibrium (NE) but NOT a SPNE. Explain why it is a NE but not SPNE