A. Show that if the inequality (9.7) is satisfied, the trigger strategies

 

described by (a) and (b) in Subsection 9.1.1 define a subgame-perfect equilibrium

of the infinitely repeated game with discounted payoffs.

B.Consider the linear environment given by (9.3) and (9.4) with M =

d = 1, c = 1/4, and n = 2. Determine the highest lower bound on the discount

rate δ such that the duopolists’ strategies described in Subsection 9.1.1 define a

subgame-perfect equilibrium of the infinitely repeated game. Allowing now c and

n to vary (i.e., they become parameters of the model), study howthe aforementioned

lower bound on δ changes with them.