Consider the infinitely repeated prisoners' dilemma and recall the definition of the grim-trigger strategy.

Here is the definition of another simple strategy called Tit-for-tat: Select C in the first period; in each period thereafter, choose the action that the opponent selected in the previous period.8 Is the tit-for-tat strategy profile a Nash equilibrium of the repeated game for discount factors close to one?

Is this strategy profile a subgame perfect Nash equilibrium of the repeated game for discount factors close to one? Explain.