Finding successful strategies for social dilemma …...Finding successful strategies for social...
Transcript of Finding successful strategies for social dilemma …...Finding successful strategies for social...
Finding successful strategies for social dilemma using K
computerYohsuke Murase, Seung Ki Baek
RIKEN Center for Computational Science, Japan Pukyong National University, Korea
I have a solution!
iterated Prisoner’s Dilemma
cooperation defection
cooperation (3,3) (0,5)
defection (5,0) (1,1)
long-term payoff
implementation error occurs with probability e<latexit sha1_base64="fSe004YKF6vMcUZEj33avSo9wuc=">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</latexit><latexit sha1_base64="fSe004YKF6vMcUZEj33avSo9wuc=">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</latexit><latexit sha1_base64="fSe004YKF6vMcUZEj33avSo9wuc=">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</latexit><latexit sha1_base64="fSe004YKF6vMcUZEj33avSo9wuc=">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</latexit>
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player A
player B
Strategies for IPD gameTit-For-Tat (TFT) Win-Stay-Lose-Shift (WSLS)It is guaranteed that your payoff is no less than the co-players'.
Cooperation is fragile against an error.
Cooperation is tolerant against an error.
Repeatedly exploited against AllD.
c
c
c d
c c
c d
d c
c
d
Other strategies (TF2T, ZD strategies, generous TFT…) have positives and negatives.
dc d
d
c
ddd
partners or rivals?
defensibleefficient
successful
AllC AllD
generous TFT
generous ZD
WSLS
TF2T
extortionate ZD
TFT
Trigger
more cooperations more defections
It would be great if a single strategy satisfies these advantages simultaneously.
=> Nash equilibrium with a guarantee that you'll never lose.
(partner) (rivals)Efficiency
⌦
⌦
⌦cooperation
Defensibility
�⌦
???
A solution for Prisoner’s Dilemma
comprehensive search in Memory-2 strategies
Yi et al., J. Theor. Biol. (2017)
4 out of 65,536 strategies satisfies the conditions
It is indeed possible to realize cooperation without exposing themselves to the risk of being exploited.
TFT-ATFT
What about n-person public-goods game?
n=3 the number of defecting co-players
Murase & Baek, J.Theor.Biol. (2018)
TFT-ATFT does not work for n=3. Does a solution exist for n=3?
Enumeration using K-computer
22nm
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n=3, m=1 : 256n=3, m=2 : 1,099,511,627,776 (2^40)
Enumeration of strategies1,099,511,627,776# of m=2 strategies
Defensibility against AllD 805,306,368
Efficiency 0Efficiency
⌦
⌦
⌦cooperation
Defensibility 3,483,008Defensibility
�⌦
Impossibility for m=2
AllDTFTAllCAON
TF2T
memory-2 strategies
no successful strategy exists in memory-2 strategy space.
0 / 1,099,511,627,776
No solution for n=3 game? or The solution exists when m>2?
Memory-3 strategies
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497323236409786642155382248146820840100456150797347717440463976893159497012533375533056
=
comparable to the number of protons in the universe
Although direct enumeration is impossible,we found there are at least 256 solutions!
Enumeration of strategies
1,099,511,627,776# of m=2 strategies
Defensibility against AllD
Defensibility 3,483,008
805,306,368
“Partially” Successful Strategies (PS2)
“Partial” Efficiency (pcooperation> 0) 544Efficiency
⌦
⌦
⌦cooperation
Defensibility
�⌦
Distinguishability 256Distinguishability
>⌦
AllC
AllC
elevating m=2 PS2 to m=3 successful strategies
24_cddccc
B
B&CB
C
B
C
B C
0_cccccc
34_dcccdc
25_cddccd
12_ccddcc
46_dcdddc
4_cccdcc
40_dcdccc
22_cdcddc
3_ccccdd
43_dcdcdd
1_cccccd
10_ccdcdc37_dccdcd
48_ddcccc 58_dddcdc
16_cdcccc
63_dddddd
23_cdcddd
41_dcdccd35_dcccdd
11_ccdcdd
29_cdddcd
44_dcddcc14_cccddc38_dccddc
53_ddcdcd50_ddccdc 26_cddcdc
56_dddccc
31_cddddd
15_ccdddd
5_cccdcd17_cdcccd
20_cdcdcc
47_dcdddd59_dddcdd
62_dddddc
61_ddddcd
60_ddddcc
55_ddcddd
51_ddccdd
Successful strategies indeed exists when m=3. Full cooperation is achieved
while keeping the defensibility and the distinguishability.
AllDTFTAllCWSLS
TF2T
defensible strategiesefficient strategiesEfficiency
⌦
⌦
⌦cooperation
Defensibility
�⌦
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An example of successful strategies.
memory length and # of players
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n=2 : TFT-ATFT (m=2) n=3 : m=3 Successful Strategies ...
for general n (>=3), we show
There is a critical memory length above which a fundamentally new class of strategies may exist.
# of players
mem
ory
leng
th
(3,3)
(2,2)
must be satisfied.
Murase & Baek, J.Theor.Biol. (2018)
Conclusions• A new class of Nash equilibrium strategies was found with the aid
of the K computer. • Well-computed strategies can solve social dilemma without
appealing to our moral.
• Y. Murase & S.K. Baek, “Seven rules to avoid the tragedy of the commons”, J. Theor. Biol. 449 p94 (2018) • Y. Murase & S.K. Baek, “Automata representation of successful strategies for social dilemmas”, arXiv:1910.02634,
under review • Y. Murase & S.K. Baek, “Memory-three strategies that are partners as well as rivals”, in preparation
References
Exploring a broader strategy space does make a difference.• public-goods game for n>3 • perception error • multiple choice of actions • indirect reciprocity • network reciprocity