Not-So-Grim Trigger: Consider the infinitely repeated Prisoner's Dilemma with discount factor δ.

Instead of using grim-trigger strategies to support a pair of actions (a­₁, a₂) other than (F, f ) as a subgame-perfect equilibrium, assume that the players wish to choose a less draconian punishment called a "length-T punishment" strategy. If there is a deviation from (a₁, a₂) then the players will play (F, f ) for T periods and then resume playing (a₁, a₂). Let δ_T be the critical discount factor so that if δ>δ_T then the adequately defined strategies will implement the desired path of play with length-T punishment as the threat.

a. Let T = 1. What is the critical value δ₁ to support the pair of actions (M,m) played in every period?

b. Let T = 2. What is the critical value δ_T to support the pair of actions (M,m) played in every period?

c. Compare the two critical values in (a) and (b). How do they differ and what is the intuition for this?