HPCを用いた進化ゲーム理論研究村瀬洋介（理化学研究所 計算科学研究センター）

2023/10/31 HPCIC計算科学フォーラム

内容• ゲーム理論、進化ゲーム理論の概要• 繰り返し囚人のジレンマにおける負けないことが保証された直接互恵戦略• 今後の展望ゲーム理論: 意思決定の科学• ゲーム理論• 複数の意思決定主体の行動を記述する数学的枠組み• John von Neumann, Oskar Morgenstern 「ゲームの理論と経済行動」(1944) が始まり

• 経済学、社会学、政治学

http://www.lanl.gov/history/atomicbomb/images/NeumannL.GIF• 進化生物学• John Maynard Smith 進化ゲーム理論• 計算機科学• 分散処理、マルチエージェント学習
CC 表示-継承 3.0
https://commons.wikimedia.org/wiki/File:John_Maynard_Smith.jpg

囚人のジレンマ
cooperation

defection

cooperation

(3,3)

(0,5)

defection

(5,0)

(1,1)

• 戦略: 協力、裏切りをプレイヤーが選択する• 互いに裏切りあう状況が唯一のNash均衡• 自分が行動を変えるインセンティブがない安定した状態（物理系でいうと局所安定状態みたいなもの）• 個人の利得の最適化 ≠ 社会全体の利得の最適化• 社会的ジレンマ、コモンズの悲劇、合成の誤謬• 地球温暖化、自然破壊、乱獲、過放牧、公共の施設の利用、買い占め、パンデミック下での行動変容

協力行動の進化• 協力行動：コストを払って、相手に利益を与える (b > c)
• なぜ協力行動が進化した？
C

-c

D ◆

✓
cooperate(C)b - c -cdefect(D)b<latexit sha1_base64="/pB32AQlMw/eMMlLHCra1I8UD1w=">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</latexit>

+b

近親選択

ネットワーク（空間）互恵

直接互恵
グループ選択間接互恵

内容• ゲーム理論、進化ゲーム理論の概要• 繰り返し囚人のジレンマにおける負けないことが保証された直接互恵戦略• 今後の展望iterated Prisoner’s DilemmaSocial Dilemma : social optimum ≠ individual bene t

player B
cooperation

defection

cooperation

(3,3)

(0,5)

defection

(5,0)

(1,1)

player A

repeated the interaction => cooperation may be a rational choice.

long-term payoff in the repeated game1(t)fi ⌘ lim lim
Fi
e!0 T !1 T
t=0<latexit sha1_base64="CfD1qyKg0ws1VkAs+U8zHbmbHOk=">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</latexit>

fi

T
X1

well known strategies
Tit-for-Tat

History
C,C
C,D
D,C
D,D

c
c

c
c

Next moveC
D
DC

tolerant against an error

your payoff is no less than the other's
TFT

History
C,C
C,D
D,C
D,D

Win-Stay-Lose-Shift

Next moveCDCD

c d d cd d c cWSLS c

c

c d

c c

WSLS cc

d d c cIt can exploit naive cooperator.

fragile against an error
TFT

c

c

c d c dWSLS ccd d d d

TFT

c

c

d

AllC

c

c c c cc d c

cweak against defectors

It cannot exploit naive cooperator.
TFT

c

c

c

c c

AllC

c

c

c

c

c

c c

WSLS c d

c d

AllD

d d d d

d

d

c

d

Zero-Determinant Strategy
Press&Dyson PNAS (2012)

extortionate ZD strategy

History
C,C
C,D
D,C
D,D

sB (0,5)(3,3)

It is guaranteed that your payoff is noless than the co-players'.

Cooperation is not maintained.

probability of C
p
q
r
s

(1,1)

(5,0)
sA

longer memory strategies
Tit-for-2Tat

All-or-Nothing
generalization of WSLS

tolerant against an error
TF2T

c c d c c

TF2T

c c c c cweak against alternating defector
TF2T

tolerant against an error

Fragile against AllD.

c c c c cdefector c d c d cHilbe et al. PNAS(2017)

Hilbe et al., Nat.Hum.Behav. (2018)

partners or rivals
(a)
AllC

TF2T

(b) eﬃcient

WSLS

TFT

generous ZD

extortionate ZD(c) partners

(S,T)

(S,T)

(R,R)

(S,T)

(R,R)

(R,R)

(R,R)

B’s payoﬀ
(P,P)

(P,P)

(T,S)

A’s payoﬀ(e) rivals(d) friendly rivals

(S,T)

(P,P)

⌦

AllD

B’s payoﬀ⌦

GRIM

B’s payoﬀ

cooperation

B’s payoﬀ⌦

generous TFT

(P,P)

(T,S)

A’s payoﬀ(T,S)

A’s payoﬀ(T,S)

A’s payoﬀ

It would be great if a single strategy works as a partner as well as a rival.

friendly rivals

cooperative Nash equilibrium with a guarantee of never being defeatedTFT-ATFT: a friendly rival strategy
Yi et al., J. Theor. Biol. (2017)• # of Memory-1 strategies: 16• => no strategy satis es the criteria• # of Memory-2 strategies: 2^16 = 65536

fi• Eight FRs were found.

Games with more than two players?
Y. Murase et al., J. Theor. Biol. (2018)

3-person public goods game

payoff matrix
PartnerEﬃciency

Rivalry

Defensibility⌦⌦⌦

cooperation⌦

TFT-ATFT does not work.

22

nm 1,099,511,627,776 strategies

京 (スーパーコンピュータ). (2023, September 27). In Wikipedia. https://
ja.wikipedia.org/wiki/%E4%BA%AC_(%E3%82%B9%E3%83%BC%E3%83%91%E3%83%BC%E3%82%B3%E3%83%B3%E3%83%94%E3%83%A5%E3%83%BC%E3%82%BF)

Enumeration of strategies
1,099,511,627,776# of m=2 strategies

805,306,368

Defensibility against AllD

Ef ciency

3,483,008⌦

Eﬃciency

⌦

AON
AllC

Defensibility

Defensibility

Impossibility : no friendly rival in memory-2
strategies.

⌦

cooperation2<latexit sha1_base64="KhAflYuw8dXnZ1exLY4273vfmLE=">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</latexit>

288

497323236409786642155382248146820840100456150797
347717440463976893159497012533375533056

comparable to the number of protons in the universe

fi

TF2T

0

⌦

What about memory-3 strategies?

TFT

AllD

partially successful strategy
1,099,511,627,776# of m=2 strategies

805,306,368

Defensibility against AllD
Defensibility

Defensibility

3,483,008⌦

Eﬃciency“Partial” Ef ciency (pcooperation> 0)⌦⌦

cooperation

Distinguishability

Distinguishability

⌦

>

⌦

AllC

AllC

“Partially” friendly rival strategies

fi

544
256

24_cddccc
48_ddcccc

37_dccdcd
10_ccdcdc

16_cdcccc

C

0_cccccc
34_dcccdc

40_dcdccc
B

25_cddccd
B

58_dddcdc

CB

12_ccddcc

4_cccdcc

46_dcdddc

22_cdcddc

1_cccccd

3_ccccdd

B&C

B

60_ddddcc

43_dcdcdd

C

20_cdcdcc

44_dcddcc

11_ccdcdd
14_cccddc

38_dccddc

62_dddddc

41_dcdccd

35_dcccdd

61_ddddcd
29_cdddcd

23_cdcddd

17_cdcccd

63_dddddd

59_dddcdd

5_cccdcd

55_ddcddd

51_ddccdd

47_dcdddd

31_cddddd
50_ddccdc

53_ddcdcd

56_dddccc

26_cddcdc

15_ccdddd

An example of friendly rival strategies.

<latexit sha1_base64="95WLehzbGYYlQYuq9vfp16ljsEs=">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</latexit>

256
2288

WSLS
AllC

TFT

AllD

TF2T
Eﬃciency⌦

Defensibility⌦

cooperation⌦

ef cient strategies

rival strategies⌦fiFriendly rival strategies are found.
Mutual cooperation is reached with probability 1
while keeping the defensibility and the distinguishability.

interpretation of m=3 successful strategies
Y. Murase et al., Sci.Rep. (2020)

an intuitive interpretation is lacking

cooperation

action table
History

Next move

C,C

C

C,D

D

D,C

C

D,D

cc

cc

D

cd

cc

cd

0

cd

dc

cc
dd
dc

dc
dc

dd

dd

cd

dd
1
defectionfiCore idea: Deterministic Finite Automaton minimization
convert a strategy de ned by an action table into the equivalent automaton having minimum number of states

Y. Murase et al., Sci.Rep. (2020)δ

72

ccc,ccdcdc
cdd dcd

cdc

ccd,cdc,
α
cdd

8

cdd
dcc

dcd
dcc

ddc

64

76

ddc
ddd
ddc

ddc

1
dcc

ddd

ddc

dcd,ddd

67

dcd

dcc
dcc

dcd
ddd

9

ccd

γ

66
ddd

cdd

β
ccc

dcc

65

ccc,cdc
ccd0γ

ddc,ddd

ccc

δ

dcd

memory length vs the number of players
Y. Murase et al., J. Theor. Biol. (2018)

n=2 : TFT-ATFT (m=2)
n=3 : memory-3 friendly rival strategies...

for general n (>=3), we showm<latexit sha1_base64="En7TK770IIYn3eKi5faMAC8QzmU=">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</latexit>nThere is a critical memory length above which
friendly rivals may exist.

r
e
w
l lo

t

a
c
i
t
e
heor

FUSS
TFT-ATFTdnuboY. Murase et al., Sci. Rep. (2020)

two-player memory-three strategies# of memory-m strategies:22

2m m=1 : 0 / 256

m=2 : 4 / 65,536
m=3 : ? / 18,446,744,073,709,551,616

w

l lo
a
c
i
t
ore

the

FUSS
TFT-ATFT

und
o
b
er

Y. Murase et al., J. Theor. Bio. (2018)

checking rivalry
It is guaranteed that the long-term payoff is no lessthan any of co-players' payoff.

Rival
⌦

existence of a negative cycle in the state transition graphe.g. TFT strategy in 2-person game

0e.g. WSLS strategy in 2-person game

-1

0

-1

c,c

c,d

c,c

c,d

d,c

d,d

d,c

d,d

+1

0

+1

0

Floyd-Warshall algorithm

WSLS
AllC

TFT

AllD

TF2T
Eﬃciency⌦

Defensibility⌦

cooperation⌦

ef cient strategies

戦略を完全二分木で表現する。葉が戦略。ノードが戦略の共通部分に対応できるだけ早く枝刈りができるように、rivalryとef ciencyを同時にチェックするfi

fi

二分木を作るときの順番（どのビットから固定するか）も重要

rival strategies⌦

Y. Murase et al., Sci. Rep. (2020)

two-player memory-three strategies# of memory-m strategies:22

2m m=1 : 0 / 256

m=2 : 4 / 65,536
m=3 : ? / 18,446,744,073,709,551,616

w

l lo
a
c
i
t
ore

the

FUSS
TFT-ATFT

We found4,261,844,305,281
friendly rival strategies.

und
o
b
er

22

cc

0

cd
dc

cd

1
dc

dc

dc

16

dd

cc

cd

dc

9

most of the strategies are noteasy to interpret...

13

dd

dd

26

37

cc
dc

11
dd

cd

(ccc,ccc)↓(ccd,ccc)

8

dd

cd

cc

dd

12
dc

dd

cc

2

cc
27
cd

dc
dd

31

dc

23

dd

32

dc

8

(ccc,ccc)→(ccd,ccc)

19

21

cd

cc

cd

13

cd

dd

cc

dc
dd

14
dd

dc
dc

dd

dd

35

12

cd

10

cd

25

dd
dc

3

dc
dc

dc

dc

2

cc

cc

16

cc

59

cd

cc

cc

dd

cd

cd

17

0

cc

dc
dd

1

56

dd
dd

Y. Murase et al., Sci. Rep. (2020)

CAPRI: a simple friendly rival
memory-3 strategy described by the ve rules

C
A
P
R
I

ooperate at mutual cooperation.
ccept punishment when you made a mistake.

CAPRI c c

c

c

c c

CAPRI c

c

c

c c

c

conduct punishment

CAPRI c

c

c d

c c

CAPRI c

c

d

c c

c

unish co-player and then forgive him.
ecover cooperation when someone cooperated.

fin all the other cases, defect.

accept punishment

CAPRI d

d d

c

c c

d

d

c

c

c c

CAPRI d

d

d d d

d

d

d d d ddY. Murase et al. Plos.Comp.Biol. (2021)

CAPRI-n: generalization to n-players game

C
A
P
R
I

t⇤ = tooperate at mutual cooperation

ccept punishment when relative payoff is highest

t

1

AND

m  t⇤ < t

1t⇤ < tAND

Nd < nNd < nC

A(relative payoﬀ) ≥ 0
against all co-players

Runish co-player when relative payoff is lower
ecover cooperation when the others cooperatedP

n all the other cases, defect.

I

Nd

m

n AND t⇤tm(relative payoﬀ) < 0
against a co-playerIwhen all coplayers
cooperated
at mutual
defection

Y. Murase et al. Plos.Comp.Biol. (2021)# of players vs memory length
relationship between memory length m and the number of players n
m = 2n1

Y. Murase et al. Plos.Comp.Biol. (2021)

CAPRI-n
l
a
c
i
t
e
r
o
the
Y. Murase et al. Sci.Rep. (2020)
S.D. Yi et al. J. Theor. Biol. (2017)

CAPRI

FUSS

No friendly rival
X
TFT-ATFT

dY. Murase et al. J. Theor. Biol. (2018)
n
u
o
b
r
e
low

m
<latexit sha1_base64="ewalGOPnfHcux7gQphZQaoD6wRY=">AAACa3ichVG7SgNBFD1Z3/GRaBpRi2CIWIVZCSpWQRvLaMwDkhB21zEu2Ze7m4AGf8DSxiI2CiLiZ9j4Axb5BBGrCDYW3mwWRIN6l9k5c+aeO2fuyJamOi5j7YAwMDg0PDI6FhyfmJwKhadnco5ZtxWeVUzNtAuy5HBNNXjWVV2NFyybS7qs8bxc2+ru5xvcdlTT2HOPLV7WpaqhHqiK5BJV0KOlKj+KGpVwjCWYF9F+IPogBj/SZvgWJezDhII6dHAYcAlrkODQV4QIBou4MprE2YRUb5/jFEHS1imLU4ZEbI3+VVoVfdagdbem46kVOkWjYZMyijh7Yneswx7ZPXtmH7/Wano1ul6OaZZ7Wm5VQmezmfd/VTrNLg6/VH96dnGAdc+rSt4tj+neQunpGycXnczGbry5xK7ZC/m/Ym32QDcwGm/KzQ7fbSFIDyD+bHc/yK0kxNVEcicZS236TzGKeSximfq9hhS2kUbW6/M5WrgMvAoRYU5Y6KUKAV8TwbcQ4p+AsoyD</latexit>nY. Murase et al., Sci. Rep. (2020)

Do friendly rivals evolve?
well-mixed population of N individuals
updated by imitation process

A mutant with a random strategy occasionally appears
simulation with reactive memory-1 species

Y. Murase et al., Plos Comp. Biol. (2023)

friendly rivals are evolutionarily robust
for any N, b/c, and σ.

1⇢N

for any mutant

simulation with reactive memory-1 species and CAPRI

CAPRI

larger N, b/c → partners
smaller N, b/c → rivals

Partner Rival Other
Hilbe et al., Nat.Hum.Behav. (2018)

Y. Murase et al., Plos Comp. Biol. (2023)(a) number of strategies
3
2

m2
1
0

240

65040 4x109 2x1019
CAPRI,
AON3

12

228

65040 4x109
TFT-ATFT,
AON2

TF2T

2

10

228

65040

TFT

WSLS

2

2

12

240

1

2

3

AllC,
AllD

0

(b) eﬃcient strategies(c) rival strategies(d) friendly rival strategies

3

9.6%

8.0%

7.0%

7.4%

3

17%

5.4% 0.67% 0.01%

3

0%

2

8.3%

11%

12%

7.0%

2

33%

14%

2

0%

3.2% 0.25%

0.011% 0.005% 4x10-5%

>10%
0%

0.012% 2x10-4%

1-10%
0-1%

1

0%

20%

13%

9.5%

1

50%

20%

15%

1.5%

1

0%

0%

0%

0%

0

50%

0%

17%

13%

0

50%

0%

8.3%

5.8%

0

0%

0%

0%

0%

0

1

2

3

0

1

2

3

0

1

2

3

m1

(a) well-mixed population

m1

m1

0%

m1

(b) group-structured population

FR players remember the co-player’s history
better than his or her own.

Conclusion• We found friendly rival strategies in iterated Prisoner’s dilemma and public-goods games.
• There is a critical memory lengths (strategic complexity) above which a fundamentally new class

CAPRI-nof strategies appear.

und

r bo
e
w
o
al l

retic
o
e
h
t

•
•
•
•
•

FUSS

TFT-ATFT

cooperation is robust against error (partner)
never allows any co-player to outperform you (rivalry)evolutionary robust for any environmental conditions⌦

exploit a broad range of strategies (AllC, WSLS), which prevents neutral drift
is a deterministic strategy whose actions are independent of the values of bene t or cost of
the gamefi• not only for PD but for the stag-hunt game and the snow-drift game• (2R > T+S, T > S)
• generalizable to n-players public goods gamefi•Among them, we found CAPRI that is described by ve simple rules. It has a number of desirable
properties.

CAPRI

⌦

cooperation⌦

References• Y. Murase and S.K. Baek “Seven rules to avoid the tragedy of the commons” J. Theor. Biol., 449,
94-102 (2018)• Y. Murase and S.K. Baek “Automata representation of successful strategies for social dilemmas” Sci.
Rep., 10, 13370 (2020)• Y. Murase and S.K. Baek "Five rules for friendly rivalry in direct reciprocity” Sci.Rep. 10, 16904 (2020)• Y. Murase and S.K. Baek "Friendly-rivalry solution to the iterated n-person public-goods game” Plos
Comp. Biol. (2021)• Y. Murase, C. Hilbe, S.K. Baek “Evolution of direct reciprocity in group-structured populations” Sci.
Rep., 12, 18645 (2022)• Y. Murase, S.K. Baek “Grouping promotes both partnership and rivalry with long memory in direct
reciprocity” PLoS Comp. Biol. 19(6): e1011228 (2023)

HPCを用いたゲーム理論の将来展望• これまでは解析的な理論研究や実験がメイン。いかに複雑な社会現象を単純な（手で解ける）数理モデルに落とし込むか• HPCを用いることで解析可能な問題の範囲が広がる• 望ましい特徴を持つ戦略を大規模に探索する（公理的アプローチ）• 利得の計算が簡単でない場合の解析（進化的アプローチ）• ありうる応用• 人間行動、心理的傾向や文化に見られるパターンを進化的観点から説明する• 社会システムのデザイン。（例：オンラインシステムで評判をどのように共有するべきか）• 現状• まだ黎明期。手法が系統的に確立しているわけではなく、適切な問題を見つけ、個別に計算手法を開発• 基本的に embarrassingly parallel。単純な並列でも取り組むべき研究課題は多く、重要度の高い課題から取り組んでいる