Results of the prisoner's dilemma tournament

In the project lab on the prisoner's dilemma, I asked members of the class who wrote algorithmic players of their own (as exercise 3 of the lab), to send them to me by e-mail. I have now received six players:

• In Axelrod's terminology, Moondog is nice. In early rounds, it is retaliatory and escalates punishments rapidly for repeated offenders; each unprovoked defection raises its ``anger'' level by a random amount in the range from 2 to 11 (inclusive). On the other hand, each act of cooperation reduces that level by the the number of rounds played, so that in later rounds Moondog is increasingly generous about forgiving unprovoked defections.
• Morally bereft is nice, usually retaliatory, and forgiving; it plays just like Look back except that it ignores the opponent's last-round defection whenever the number of rounds played is divisible by 3 or by 5 (that is, 7/15 of the time).
• Justice is nice, retaliatory, and sometimes forgiving. If the other player always cooperates, so does Justice; if the other player always defects, so does Justice (after the first round). If the other player sometimes cooperates and sometimes defects, then Justice responds to cooperation with cooperation and to defection by defecting 2/3 of the time and cooperating 1/3 of the time, randomly.
• Though it is coded somewhat differently, P-Funk's strategy is identical to that of Look back.
• Don is not nice (it defects in each of the first three rounds), not retaliatory, and not responsive (it cooperates in all subsequent rounds, regardless of what the other player does). Its early defections invite retaliation, and its subsequent unresponsiveness ensures that opponents that experiment with retaliatory defection are well rewarded for this strategy.
• Tyler is nice, somewhat retaliatory, and forgiving. It plays like Look back in even-numbered rounds; in odd-numbered rounds, it cooperates if the other player has cooperated in either of the preceding two rounds, and defects only if the other player has defected in both of those rounds.

Here are the results of the tournament, with 162 rounds in each match:

> (play-tournament roster)
(("Moondog" . 2427)
 ("Morally bereft" . 2423)
 ("Justice" . 2425)
 ("P-Funk" . 2425)
 ("Don" . 2405)
 ("Tyler" . 2425))

Since Moondog, Morally bereft, Justice, P-Funk, and Tyler are all nice, they all cooperate with each other consistently, each receiving three points per round, 486 points per match. The differences in their scores reflect their differing abilities to cope with Don. Morally bereft spontaneously forgives Don's third defection; Justice, P-Funk, and Tyler exact a one-round apology before returning to cooperation; Moondog requires two rounds of apology for Don's unprovoked defections in the first two rounds.

In spite of its combination of early obnoxiousness, unresponsiveness, and easy exploitability, Don does fairly well in this tournament, scoring almost 2.97 points per round, because it happens to be matched against four extremely forgiving players. If the nice but totally unforgiving Friedman player is added to the roster, the results shift markedly:

> (play-tournament roster-with-Friedman)
(("Moondog" . 2913)
 ("Morally bereft" . 2909)
 ("Justice" . 2911)
 ("P-Funk" . 2911)
 ("Don" . 2412)
 ("Tyler" . 2911)
 ("Friedman" . 3227))

All of the nice strategies pick up 486 points against Friedman, and vice versa, but the result of the Don versus Friedman match is quite lopsided:

> (play-match Don Friedman)
(7 . 797)

These results reinforce Axelrod's conclusion that players that are nice and responsive tend to do better, in most fields of players, than those that are willing to defect first and those that ignore their opponents' signals. The results also suggest that the importance of these traits is greatly lessened if the vast majority of the other players in the field are forgiving.

This document is available on the World Wide Web as

http://www.cs.grinnell.edu/~stone/courses/scheme/prisoners-dilemma-tournament.xhtml

created October 7, 2001
last revised October 11, 2001

John David Stone (stone@cs.grinnell.edu)