This is the last of three papers on computer simulations of the prisoner's dilemma game. The first paper introduced and described Robert Axelrod's approach to testing various strategies. The second paper described some of the results and conclusions of Axelrod's tests and reported on a prisoner's-dilemma tournament among players proposed by members of the class.
After describing the results of the tournament among the class's players, I asked members of the class to write up and submit revised players, reflecting the understanding gained in the tournament. Here are the strategies that were submitted for this second round:
2B4, in its revised form, cooperates in the first two rounds and thereafter does whatever the other player did two rounds earlier. (The only change from the earlier version of 2B4 is that the new version cooperates on the first round rather than defecting.)
Math defects whenever the other player has defected more often than it has cooperated, but otherwise cooperates.
Choice cooperates in the first round and plays like Look back for the next eighty rounds. After that, it cooperates in odd-numbered rounds and defects in even-numbered ones.
The Somewhat better player cooperates for the first five rounds. Subsequently, it cooperates unless the other player defected in each of the two preceding rounds.
Two players identical to Look back were submitted: Oldie but goodie and Master player.
The Defect to begin player defects on the first round and thereafter plays like Look back.
Player cooperates in the first ten rounds, then uses the Look back strategy for 151 rounds. After that, it defects in every round.
The revised version of Fair-weather friend defects in the first round. In the second round, it matches the other player's first-round play. Subsequently, it chooses, in each round, between ``probably cooperating'' and ``probably defecting'' -- in each case, choosing the probable action with probability 199/200. It ``probably cooperates'' whenever the other player has cooperated on both of the preceding two rounds and ``probably defects'' whenever the other player has defected on either of the previous two rounds.
Big cheese cooperates on the first two rounds, defects on the third, and cooperates on the next three. Subsequently, it cooperates if the other player has never defected, defects if the other player has defected sixty percent or more of the time, and otherwise matches whatever the other player did in the previous round.
The revised version of Bob cooperates in the first three rounds and continues to cooperate until the other player has defected at least twice. Subsequently, Bob defects when the other player defected in the previous round or in the third round back.
Player 2C cooperates in the first three rounds. In the fourth, fifth, and sixth rounds, it cooperates unless the other player defected in the preceding round or in both the second and third rounds back. Subsequently, it cooperates unless the other player defected in the preceding round, or in both the second and third rounds back or unless Player 2C itself defected two rounds back.
The newly revised version of Zero/two revised cooperates eighty percent of the time, as long as the other player has never defected twice in a row. Once that has happened, however, Zero/two revised cooperates only twenty percent of the time.
Of the thirteen strategies, seven (2B4, Math, Somewhat better, Oldie but goodie, Master player, Bob, and Player 2C are nice; the rest (Choice, Defect to begin, Player, Fair-weather friend, Big cheese, and Zero/two revised) are not. Only Player is unforgiving.
Here are the tournament results for these thirteen players. Each match lasted 213 rounds.
1 2 3 4 5 6 7 8 9 10 11 12 13
1 2B4 639 291 639 639 636 639 533 595 638 639 639 417
2 Math 639 252 639 639 530 639 483 530 636 639 639 498
3 Choice 301 457 457 336 333 336 348 333 339 339 339 464
4 Somewhat better 639 639 252 639 636 639 533 633 636 639 639 508
5 Oldie but goodie 639 639 331 639 530 639 534 530 638 639 639 372
6 Defect to begin 641 535 333 641 535 535 536 213 640 641 641 343
7 Master player 639 639 331 639 639 530 534 530 638 639 639 328
8 Player 543 743 323 543 539 536 539 533 536 543 539 350
9 Fair-weather 605 535 333 643 535 213 535 538 540 641 641 352
10 Big cheese 638 641 329 641 638 635 638 536 530 641 638 422
11 Bob 639 639 329 639 639 636 639 533 636 636 639 377
12 Player 2C 639 639 329 639 639 636 639 534 636 638 639 404
13 Zero/two revised 427 733 269 683 377 338 333 315 352 222 227 234
Somewhat better 7032
Player 2C 7011
Bob 6981
2B4 6944
Big cheese 6927
Oldie but goodie 6769
Math 6763
Master player 6725
Player 6267
Defect to begin 6234
Fair-weather 6111
Zero/two revised 4510
Choice 4382
A total of 16614 rounds of the prisoner's dilemma were played. The average combined score per round was 4.73 -- a significant improvement from the first tournament. (I conclude that you designers learned something from experience.) If all players had cooperated consistently, each would have scored 7668 points.
The only surprise was that the non-nice player Big cheese managed to finish in fifth place, ahead of three nice players, including both duplicates of Look back. Big cheese scored extra points by ignoring early defections by Defect to begin and Zero/two revised, which the more retaliatory Oldie but goodie, Math, and Master player felt compelled to punish.
This document is available on the World Wide Web as
http://www.math.grin.edu/~stone/courses/scheme/dilemma-project-3.html
created July 17, 1997
last revised October 6, 1997