ANSWER ONLY THE BONUS (NOT PART A,B)

Consider the following prisoners' dilemma: (a) What, if any, are the pure strategy Nash equilibria? Show your work to justify your answer. What about mixed strategy? If there are any, find them and show how you found them; if there are no mixed strategy Nash equilibria, show why there are not any. (b) Suppose this game is repeated twice, what are the subgame perfect equilibria. Now suppose the game is repeated an infinite number of times. Can (Collude, Collude) each period, be the outcome of a subgame perfect Nash equilibrium? And if so under what circumstances? Bonus In question 4 , Consider the following sequence of play: CD,DC,CD,DC, where CD means player 1 chooses Collude and Player 2 chooses Don't, and DC means the reverse. Can that ever be the outcome of a subgame perfect Nash equilibrium? If so, under what circumstances; if not, why not? Consider the following prisoners' dilemma: (a) What, if any, are the pure strategy Nash equilibria? Show your work to justify your answer. What about mixed strategy? If there are any, find them and show how you found them; if there are no mixed strategy Nash equilibria, show why there are not any. (b) Suppose this game is repeated twice, what are the subgame perfect equilibria. Now suppose the game is repeated an infinite number of times. Can (Collude, Collude) each period, be the outcome of a subgame perfect Nash equilibrium? And if so under what circumstances? Bonus In question 4 , Consider the following sequence of play: CD,DC,CD,DC, where CD means player 1 chooses Collude and Player 2 chooses Don't, and DC means the reverse. Can that ever be the outcome of a subgame perfect Nash equilibrium? If so, under what circumstances; if not, why not