Table 1 Summary results for our comparison of algorithms

From: Cooperating with machines

Algorithm

Round-Robin average

% Best score

Worst-case score

Replicator dynamic

Group-1 Tourney

Group-2 Tourney

Rank summary min–mean–max

S++

1, 1, 1

2, 1, 2

1, 1, 1

1, 1, 1

1, 1, 2

1, 1, 1

1–1.2–2

Manipulator

3, 2, 3

4, 3, 8

5, 2, 4

6, 4, 3

5, 3, 3

5, 2, 2

2–3.7–8

Bully

3, 2, 1

3, 2, 1

7, 13, 20

7, 3, 2

6, 2, 1

6, 3, 5

1–4.8–20

S++/simple

5, 4, 4

8, 5, 9

4, 6, 10

10, 2, 6

8, 4, 6

9, 4, 6

2–6.1–10

S

5, 5, 8

6, 7, 10

3, 3, 8

5, 5, 8

7, 5, 9

7, 5, 9

3–6.4–10

Fict. play

2, 8, 14

1, 6, 10

2, 8, 16

3, 12, 15

2, 8, 12

4, 9, 14

1–8.1–16

MBRL-1

6, 6, 10

5, 4, 7

8, 7, 14

11, 11, 13

9, 7, 10

8, 7, 10

4–8.5–14

EEE

11, 8, 7

14, 9, 5

9, 4, 2

14, 10, 9

13, 9, 8

13, 10, 8

2–9.1–14

MBRL-2

14, 5, 5

13, 8, 6

19, 5, 3

18, 9, 4

18, 6, 5

18, 6, 4

3–9.2–19

Mem-1

6, 9, 13

7, 10, 21

6, 9, 17

2, 6, 10

3, 10, 17

2, 8, 15

2–9.5–21

M-Qubed

14, 20, 4

15, 20, 3

15, 19, 5

17, 19, 5

17, 21, 4

16, 21, 3

3–13.2–21

Mem-2

9, 11, 20

9, 11, 22

13, 17, 22

4, 13, 19

4, 13, 25

3, 12, 20

3–13.7–25

Manip-Gf

11, 11, 21

12, 12, 19

12, 11, 19

9, 7, 20

12, 14, 20

11, 13, 21

7–14.2–21

WoLF-PHC

17, 11, 13

18, 14, 14

18, 14, 18

16, 14, 14

16, 11, 11

15, 11, 11

11–14.2–18

QL

17, 17, 7

19, 19, 4

17, 18, 7

19, 18, 7

19, 20, 7

19, 18, 7

4–14.4–20

gTFT

11, 14, 22

11, 15, 20

11, 16, 23

8, 8, 22

10, 16, 21

10, 15, 22

8–15.3–23

EEE/simple

20, 15, 11

20, 17, 12

20, 10, 9

20, 16, 11

24, 15, 14

20, 16, 13

9–15.7–24

Exp3

19, 23, 11

16, 23, 15

16, 23, 6

15, 23, 12

15, 25, 13

17, 25, 12

6–17.2–25

CJAL

24, 14, 14

25, 14, 13

24, 12, 15

24, 17, 16

20, 12, 16

22, 14, 16

12–17.3–25

WSLS

9, 17, 24

10, 16, 24

10, 20, 24

12, 20, 24

11, 17, 24

12, 17, 25

9–17.6–25

GIGA-WoLF

14, 19, 23

17, 18, 23

14, 15, 21

13, 15, 23

14, 18, 22

14, 19, 23

13–18.1–23

WMA

21, 21, 15

21, 21, 16

22, 21, 12

22, 21, 17

21, 19, 15

23, 20, 17

12–19.2–23

Stoch. FP

21, 21, 15

22, 22, 17

23, 22, 11

23, 22, 18

25, 24, 18

25, 22, 18

11–20.5–25

Exp3/simple

21, 24, 16

23, 24, 18

21, 24, 13

21, 24, 21

22, 22, 19

21, 23, 19

13–20.9–24

Random

24, 25, 25

24, 25, 25

25, 25, 25

25, 25, 25

23, 23, 23

24, 24, 24

23–24.4–25

  1. This summary gives the relative rank of each algorithm with respect to each of the six performance metrics we considered, at each game length. A lower rank indicates higher performance. For each metric, the algorithms are ranked in 100-round, 1000-round, and 50,000-round games, respectively. For example, the 3-tuple 3, 2, 1 indicates the algorithm was ranked 3rd, 2nd, and 1st in 100, 1000, and 50,000-round games, respectively. More detailed results and explanations are given in Supplementary Note 3
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