Represent each of the following strategies for an infinitely repeated Prisoner's Dilemma in an automaton diagram like those discussed in class.

a. Choose C in period 1 and after any history in which the other player chose C in every period except, possibly, the previous period; choose D after any other history. (That is, punishment is grim, but its initiation is delayed by one period.)

b. Choose C in period 1 and after any history in which the other player chose D in at most one period; choose D after any other history. (That is, punishment is grim, but a single lapse is forgiven.)

c. (Pavlov, or win-stay, lose-shift) Choose C in period 1 and after any history in which the outcome in the last period is either (C,C) or (D,D); choose D after any other history. (That is, choose the same action again if the outcome was relatively good for you, and switch actions if it was not.)

d. For each of these three strategies s, determine the values of , if any, for which the strategy pair (s, s) is a Nash equilibrium of the infinitely repeated version of the following game:

CD

C 2,2 0,3 D 3,0 1,1

For each strategy s for which there is no such value of , determine whether there are any other payoffs for the Prisoner's Dilemma such that for some the strategy pair (s, s) is a Nash equilibrium of the infinitely repeated version of this modified version of the game.