define a subgame-perfect equilibrium of the infinitely repeated game with discounted payoffs.

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 =

= 1, = 1/4and = 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 and

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

lower bound on δ changes with them.

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