ECON2112
PROBLEM SET 3
DUE: 1st April(MONDAY)
Instructions
Please write your name and student ID on the top of assignment
Please submit a pdf document.
Exercise 1 (6 marks)
Ashok (A) and Beatrice (B) are a two-member team in an IT fum. Ashok decides first whether to
work on difficult problems (D) or easy problems (E). Subsequently, Ashok and Beatrice choose
their own effmt levels.
We assume that the effort choices are made separately but simultaneously. Let XA and X8
denote the level of effort exerted by Ashok and Beatrice respectively. Both XA and Xs can take
only two values: 4 or 10. That is X; E {4, 10} for i = A, B.
If Ashok chooses E
• Ashok gets max {XA, Xs} -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, 4Xs} -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