Exercise 1
a) Pure strategy nash equilibrium in this case is Not Buy, bad ( 0,0) as no one wants to deviate from this strategy.
b) The player chooses buy in the first period and chooses buy in the next 9 periods if the opponent chooses good upto that point else choose not buy from the subsequent periods.
c) Alice should play buy in the first period and in all periods to come if the opponent chooses good. She should play not buy if good is not chosen in any period.
d) If the opponent sustains good outcome in all periods he receives
2/1-r
Now if he deviates then he receives 3 in one period and 0 in all periods to come.
2/1-r≥ 3 + 0 to sustain the cooperative equilibrium.
e) Now we have an additional constraint which can be expressed as:
0.30(2/1-r) ≥ 0.70(3)
If this condition is satisfied the game will be continued and cooperative equilibrium will be maintained.