1. Robert Axelrod’s Tournaments Robert Axelrod’s Tournaments, as reported in Axelrod, Robert. 1980a. “Effective Choice in the Prisoner’s Dilemma.” Journal of Conflict Resolution 24: 3-25. Axelrod, Robert. 1980b. “More Effective Choice in the Prisoner’s Dilemma.” Journal of Conflict Resolution 24 (3): 379-403. Axelrod, Robert. 1984. Evolution of Cooperation. Robert Axelrod’s Tournaments Robert Axelrod’s Tournaments, as reported in Axelrod, Robert. 1980a. “Effective Choice in the Prisoner’s Dilemma.” Journal of Conflict Resolution 24: 3-25. Axelrod, Robert. 1980b. “More Effective Choice in the Prisoner’s Dilemma.” Journal of Conflict Resolution 24 (3): 379-403. Axelrod, Robert. 1984. Evolution of Cooperation.

2. Tournament Num. 1 Tournament Num. 1 (1980) -non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1) -round robin tournament (play all other entrants, twin, and RANDOM) -each entrant told to write a program to select C or D choice every move, can use history of the game so far in this decision making -sent copies of preliminary tournament in which TFT scored second, so known to be powerful competitor, also told RANDOM was somewhere in the competition  tried to improve on TFT principle -known number of moves per game: 200 -entire round robin run 5 times  total 120,000 moves and 240,000 choices Tournament Num. 1 Tournament Num. 1 (1980) -non-zero sum setting, given payoff matrix (R=3, T=5, S=0, P=1) -round robin tournament (play all other entrants, twin, and RANDOM) -each entrant told to write a program to select C or D choice every move, can use history of the game so far in this decision making -sent copies of preliminary tournament in which TFT scored second, so known to be powerful competitor, also told RANDOM was somewhere in the competition  tried to improve on TFT principle -known number of moves per game: 200 -entire round robin run 5 times  total 120,000 moves and 240,000 choices

3. 14 Entrants -3 countries, 5 disciplines (psychology, math, economics, sociology, political sciences) -scores range from 0 to 1000, but “useful benchmark for very good performance is 600,” attained if both always cooperate together -“very poor performance [benchmark] is 200 points” (if both always D) -winner Tit for Tat (TFT) scored 504 (but if change P=2, does not win) -top 8 entries were nice (defined as not first to defect), rest were not -nice entries’ scores scored from 472 to 504, while best of mean entries only scored 401 points (huge disparity!) -logically, because nice ones cooperate together, this is how TFT wins! (though it cannot get a score higher than its opponent’s) 14 Entrants -3 countries, 5 disciplines (psychology, math, economics, sociology, political sciences) -scores range from 0 to 1000, but “useful benchmark for very good performance is 600,” attained if both always cooperate together -“very poor performance [benchmark] is 200 points” (if both always D) -winner Tit for Tat (TFT) scored 504 (but if change P=2, does not win) -top 8 entries were nice (defined as not first to defect), rest were not -nice entries’ scores scored from 472 to 504, while best of mean entries only scored 401 points (huge disparity!) -logically, because nice ones cooperate together, this is how TFT wins! (though it cannot get a score higher than its opponent’s)

4. 14 Entrants -important to be nice and forgiving -2 kingmakers (defined as players who do not do well themselves but “LARGELY determine the rankings among the top contenders”): GRAASKAMP and DOWNING -DOWNING most important kingmaker since it had the largest range of scores achieved with the nice rules, important to note DOWNING was not based on TFT principle -now to look at the actual results!, then to examen the strategies, since strategies aside from TFT are just denoted by name of creator 14 Entrants -important to be nice and forgiving -2 kingmakers (defined as players who do not do well themselves but “LARGELY determine the rankings among the top contenders”): GRAASKAMP and DOWNING -DOWNING most important kingmaker since it had the largest range of scores achieved with the nice rules, important to note DOWNING was not based on TFT principle -now to look at the actual results!, then to examen the strategies, since strategies aside from TFT are just denoted by name of creator

6. STRATEGIES! 1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto (psychology), as we all know- cooperates on first move, then does what opponent did last move, “eye for eye” style, 4 lines FORTRAN 2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics), begins with cooperation/ TFT, but after opponent finishes second run of D, institutes extra punishment  increases number of punishments (D) by 1 with each run of opponent’s defections, then decides whether to give opponent a fresh start and begin with TFT again based on- if it has 10+ points more than opponent, opponent has not started another run of D’s, been 20+ moves since last fresh start, are 10+ moves left, number of opponent’s D’s “differs from 50-50 generator by at least 3 standard deviations,” 41 lines of code STRATEGIES! 1. Tit for Tat (TFT)- winner with 504.5 points, from Toronto (psychology), as we all know- cooperates on first move, then does what opponent did last move, “eye for eye” style, 4 lines FORTRAN 2. TIDEMAN and CHIERUZZI- 500.4 points, from US (Economics), begins with cooperation/ TFT, but after opponent finishes second run of D, institutes extra punishment  increases number of punishments (D) by 1 with each run of opponent’s defections, then decides whether to give opponent a fresh start and begin with TFT again based on- if it has 10+ points more than opponent, opponent has not started another run of D’s, been 20+ moves since last fresh start, are 10+ moves left, number of opponent’s D’s “differs from 50-50 generator by at least 3 standard deviations,” 41 lines of code

7. STRATEGIES! 3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless it was only one to C on first move and only one to D on second move, then it will D on third move, after third move- it chooses based on a complex weighted sum (2 points for opponent’s D, 1 point for own D, then weight this sum for past three terms- 16 for last term, then 4, then 1; if sum = 63, i.e. three turns of mutual defection  it will C) 4. GROFMAN- 481.9 points, always cooperates unless players did not do the same thing on the last move, then cooperates with prob 2/7 5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it defects once, if other defects again- it begins again with cooperation, in general- “length of retaliation is increased by one for each departure from mutual cooperation” STRATEGIES! 3. NYDEGGER- 485.5 points, starts with TFT for first 3 moves unless it was only one to C on first move and only one to D on second move, then it will D on third move, after third move- it chooses based on a complex weighted sum (2 points for opponent’s D, 1 point for own D, then weight this sum for past three terms- 16 for last term, then 4, then 1; if sum = 63, i.e. three turns of mutual defection  it will C) 4. GROFMAN- 481.9 points, always cooperates unless players did not do the same thing on the last move, then cooperates with prob 2/7 5. SHUBIK- 480.7 pts, cooperates until opponent plays D, then it defects once, if other defects again- it begins again with cooperation, in general- “length of retaliation is increased by one for each departure from mutual cooperation”

8. STRATEGIES! 6. STEIN- 477.8 pts, TFT except it cooperates always first four moves and defects on last 2 moves (move 199 and 200 of game), every 15 moves checks to see if opponent is RANDOM with chi-squared test of opponent’s transition probabilities and alternating CD/DC moves 7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it defects forever 8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 moves, then if there is a defection, it will defect forever 9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, defects on move 51, then plays 5 more TFT, check to see if opponent is RANDOM, if so- D from then on (also checks for TFT, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, enough trust STRATEGIES! 6. STEIN- 477.8 pts, TFT except it cooperates always first four moves and defects on last 2 moves (move 199 and 200 of game), every 15 moves checks to see if opponent is RANDOM with chi-squared test of opponent’s transition probabilities and alternating CD/DC moves 7. FRIEDMAN- 473.4 pts, cooperates until opponent defects, then it defects forever 8. DAVIS- 471.9 pts, last of the nice guys, cooperates first 10 moves, then if there is a defection, it will defect forever 9. GRAASKAMP- 400.7 pts, one of kingmakers, TFT for 50 moves, defects on move 51, then plays 5 more TFT, check to see if opponent is RANDOM, if so- D from then on (also checks for TFT, ANALOGY, CLONE), otherwise- randomly defects every 5-15 moves, enough trust

9. STRATEGIES! 10. DOWNING- 390.6, main kingmaker, starts with D since assumes opponent is unresponsive (i.e. initially assumes 1/2 for conditional probabilities, its downfall!), from then on- assesses and updates probabilities (that opponent cooperates if DOWNING defects, etc) to calculate choice to maximize its long-term expected payoff, if the 2 conditional probabilities have similar values- DOWNING determines pays to D, conversely- if opponent is responsive (much more likely to play C after DOWNING plays C than after D), then it will cooperate 11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of C following the other plays C to 1/2 by the 200th move 12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after D 13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 10% less than opponent has on preceding 10 moves STRATEGIES! 10. DOWNING- 390.6, main kingmaker, starts with D since assumes opponent is unresponsive (i.e. initially assumes 1/2 for conditional probabilities, its downfall!), from then on- assesses and updates probabilities (that opponent cooperates if DOWNING defects, etc) to calculate choice to maximize its long-term expected payoff, if the 2 conditional probabilities have similar values- DOWNING determines pays to D, conversely- if opponent is responsive (much more likely to play C after DOWNING plays C than after D), then it will cooperate 11. FELD- 327.6 pts, starts with TFT, gradually lowers probability of C following the other plays C to 1/2 by the 200th move 12. JOSS- 304.4, cooperates 90% after opponent’s C, always D after D 13. TULLOCK- 300.5, cooperates first 11 moves, then cooperates 10% less than opponent has on preceding 10 moves

10. Last of STRATEGIES! 14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with probability of C of 30%, which is updated every 10 moves if opponent seems very cooperative, very uncooperative, or random, after 130 moves if losing- probability is adjusted, this complex process kept P between 30% and 70%, making it seem random to most opponents 15. RANDOM- 276.3 pts, C with probability 1/2 and D with probability 1/2 (C and D with equal probabilities) Last of STRATEGIES! 14. GRADUATE STUDENT NAME WITHHELD- 282.2 pts, starts with probability of C of 30%, which is updated every 10 moves if opponent seems very cooperative, very uncooperative, or random, after 130 moves if losing- probability is adjusted, this complex process kept P between 30% and 70%, making it seem random to most opponents 15. RANDOM- 276.3 pts, C with probability 1/2 and D with probability 1/2 (C and D with equal probabilities)

11. Tournament Num. 2 Tournament Num. 2 (1980) -same non-zero sum setting, again round robin tournament (play all) -each entrant was sent report of first tournament, given same task -instead of known number of moves per game, “length of the game was determined probabilistically with.00346 chance of ending with each given move” (one way to include w), w chosen so expected median length = 200 moves (w =.99654 in second tournament) -average length turned out to be shorter: closer to 150 moves -endgame effects successfully avoided this time -features of entries do not relate to success (length of program, type, nationality, type of program, etc) Tournament Num. 2 Tournament Num. 2 (1980) -same non-zero sum setting, again round robin tournament (play all) -each entrant was sent report of first tournament, given same task -instead of known number of moves per game, “length of the game was determined probabilistically with.00346 chance of ending with each given move” (one way to include w), w chosen so expected median length = 200 moves (w =.99654 in second tournament) -average length turned out to be shorter: closer to 150 moves -endgame effects successfully avoided this time -features of entries do not relate to success (length of program, type, nationality, type of program, etc)

12. 63 Entrants -6 countries, contests largely recruited via journals, etc -everyone from first tournament re-invited, entrants ranged from 11 year-old Steve Newman to professors from many disciplines, including computer science and evolutionary biology this time -more than half of entries were nice, Tit for Tat (TFT) won again -Tit for Two Tats- too forgiving, suggested post-Tourney 1, submitted Tourney 2 by evolutionary biologist, ended up in bottom half of group -5 representative rules can predict how a given rule did with the 63 rules- GRAASKAMP & KATZEN (S 6 ), PINKLEY (S 30 ), ADAMS (S 35 ), GLADSTEIN (S 46 ), and FEATHERS (S 27 )  predicted tournament score T = 120 + (.202) S 6 + (.198) S 30 + (.110) S 35 + (.072) S 46 + (.086) S 27 63 Entrants -6 countries, contests largely recruited via journals, etc -everyone from first tournament re-invited, entrants ranged from 11 year-old Steve Newman to professors from many disciplines, including computer science and evolutionary biology this time -more than half of entries were nice, Tit for Tat (TFT) won again -Tit for Two Tats- too forgiving, suggested post-Tourney 1, submitted Tourney 2 by evolutionary biologist, ended up in bottom half of group -5 representative rules can predict how a given rule did with the 63 rules- GRAASKAMP & KATZEN (S 6 ), PINKLEY (S 30 ), ADAMS (S 35 ), GLADSTEIN (S 46 ), and FEATHERS (S 27 )  predicted tournament score T = 120 + (.202) S 6 + (.198) S 30 + (.110) S 35 + (.072) S 46 + (.086) S 27