Section 4.7 Repeated Prisoner's Dilemma
ΒΆIn this section we look at two players playing Prisoner's Dilemma repeatedly. We call this game an iterated Prisoner's Dilemma. Recall the general Prisoner's Dilemma matrix from previous sections, given again in Table 4.7.1.Player 2 | |||
Cooperate | Defect | ||
Driver 1 | Cooperate | (3,3) | (0,5) |
Defect | (5,0) | (1,1) |
Exercise 4.7.2. A single internet purchase.
Suppose the above matrix represents the situation of purchasing an item (say, a used textbook) on the internet where both parties are untraceable. You agree to send the money at the same time that the seller agrees to send the book. Then we can think of Cooperating as each of you sending money/ book, and Defecting as not sending money/ book. Why might a player Cooperate? Why might a player Defect?
Exercise 4.7.3. Repeated internet purchases.
Now suppose you wish to continue to do business with the other party. For example, instead of buying a used textbook, maybe you are buying music downloads. Why might a player cooperate? Why might a player defect? Do these resons differ from your reasons in Exercise 4.7.2?
Exercise 4.7.4. Strategy for repeated Prisoner's Dilemma.
Suggest a strategy for playing the Prisoner's Dilemma in Table 4.7.1 repeatedly. DON'T SHARE YOUR STRATEGY WITH ANYONE YET!
Exercise 4.7.5. Play Prisoner's Dilemma repeatedly.
Play 10 rounds of Prisoner's Dilemma with someone in class. Use your suggested strategy. Keep track of the payoffs. Did your strategy seem effective? What should it mean to have an βeffectiveβ strategy?
Strategy: Defection. Your strategy is to always choose DEFECT (D).
Strategy: Cooperation. Your strategy is to always choose COOPERATE (C).
Strategy: Tit for Tat. Your strategy is to play whatever your opponent just played. Your first move is to COOPERATE (C), but then you need to repeat your opponent's last move.
Strategy: Tit for Two Tats. Your strategy is to COOPERATE (C) unless your opponent DEFECTS twice in a row. After two D's you respond with D.
Strategy: Random (1/2, 1/2). Your strategy is to COOPERATE (C) randomly 50% of the time and DEFECT (D) 50% of the time. [Note: it will be hard to be truly random, but try to play each option approximately the same amount.]
Strategy: Random (3/4, 1/4). Your strategy is to COOPERATE (C) randomly 75% of the time and DEFECT (D) 25% of the time. [Note: it will be hard to be truly random, but try to play C more often than D.]
Strategy: Random (1/4, 3/4). Your strategy is to COOPERATE (C) randomly 25% of the time and DEFECT (D) 75% of the time. [Note: it will be hard to be truly random, but try to play D more often than C.]
Strategy: Tit for Tat with Occasional Surprise D. Your strategy is to play whatever your opponent just played. Your first move is to COOPERATE (C), but then you need to repeat your opponent's last move. Occasionally, you will deviate from this strategy by playing D.
Exercise 4.7.6. A Prisoner's Dilemma tournament.
WITHOUT SHARING YOUR STRATEGY, play Prisoner's Dilemma 10 times with each of the other members of the class. Keep track of the payoffs for each game and your total score.
Exercise 4.7.7. Effectiveness of your strategy.
Describe which opponents' strategies seemed to give you more points, which seemed to give you fewer?
Exercise 4.7.8. Winning strategies.
Describe the strategy or strategies that had the highest scores in the tournament. Does this seem surprising? Why or why not? How do the winning strategies compare to the strategy you suggested in Exercise 4.7.4?
Exercise 4.7.9. Rationality in repeated Prisoner's Dilemma.
How does Repeated Prisoner's Dilemma differ from the βone-timeβ Prisoner's Dilemma? Try to think in terms of rational strategies.
Exercise 4.7.10. Example of Repeated Prisoner's Dilemma in real life.
Describe a situation from real life that resembles a Repeated Prisoner's Dilemma.
Exercise 4.7.11. Only a few defectors.
How do a few defectors fare in a society of mostly cooperators? How do the cooperators fare? (In other words, who will be more successful?) Keep in mind that everyone is playing with lots of cooperators and only a few defectors. Who will have the most points, cooperators or defectors?
Exercise 4.7.12. Only a few cooperators.
How do a few cooperators fare in a society of mostly defectors? How do the defectors fare? (In other words, who will be more successful?) Keep in mind that everyone is playing with lots of defectors and only a few cooperators. Who will have the most points, cooperators or defectors?
Exercise 4.7.13. A society of TIT-FOR-TATers.
Now consider a society of mostly TIT-FOR-TATers. How do a few defectors fare in a society of mostly TIT-FOR-TATers? How do the TIT-FOR-TATers fare? How would a few cooperators fare with the TIT-FOR-TATers? Would the evolution of such a society favor cooperation or defection?