a) Suppose that Paul and Eddy play two games, the first one on Saturday and the second on Sunday. On Saturday they play the following
Prisoners' dilemma game:
Eddy
Cooperate
Paul
defect
Cooperate
100, 100
120,0
Defect
0, 120
Saturday
10, 10
On Sunday they play the following Coordination game:
Eddy
Rich
Poor
Rich
Paul
Poor
100, 100
0,0
0,0
70,70
On Friday they agree to both play Cooperate on Saturday and Rich on Sunday. They also agree that in case one of them will not play
Cooperate on Saturday, they will both play Poor on Sunday.
Assume that Paul and Eddy are profit maximisers and characterized by hyperbolic discounting with $\delta = 0.9$ (daily discount factor) and
$\beta = 0.5$.
a) (5 marks) Show that the strategy they agree on is a best response for both from the point of view of Friday.
b) (5 marks) What do they effectively play on Saturday? (Explain your answer)
c) (10 marks) Paul has also to do a homework for Monday. He can do it either on Friday, Saturday or Sunday. The cost to do it is immediate
and is 50 on Friday, 70 on Saturday and 90 on Sunday. The reward for delivering the homework is 210 and is paid on Monday. Assuming
that Paul is a sophisticated player computing his optimal strategy and state when he will do the homework.