a$)$ What is present value of playing cooperation $(C)$ in all periods against Tit$-$For$-$Tat? Write your answer in terms of the discount rate $.$

b$)$ What is the present value of playing defect $(D)$ in the first period and cooperation $(C)$ in all following periods against Tit$-$For$-$Tat? Write your answer in terms of the discount rate $.$

c$)$ For what discount factors $()$ can cooperation be sustained against Tit$-$For$-$Tat?

d$)$ What is the present value of playing cooperation $(C)$ in all periods against Grim Trigger? Write your answer in terms of the discount rate $.$

e$)$ What is the present value of playing defect $(D)$ in the first period and cooperation $(C)$ in all following periods against Grim Trigger? Write your answer in terms of the discount rate $.$

f$)$ For what discount factors $()$ can cooperation be sustained against Grim Trigger?