Victorious Warriors
Peter van Emde Boas, ILLC-FNWI-UvA and
Bronstee.com Software & Services B.V.
Logic in Sun Tzu
and the
Games played
in the Romance
of the Three
Kingdoms
Peking University
20140507
Peter van Emde Boas:
Victorious Warriors 20140507
Who am I ?
Born: 19450403 ( 4 years before foundation PRC)
MS & PhD: University of Amsterdam
supervisors: van Wijngaarden, Baayen, Hartmanis
(Turing Award winner)
Fields: Mathematics, Computer Science, Logic
50 years of professional activity
-- van Emde Boas Priority Queue
Long term involvement with mayor Conference
series (ICALP, TAMC, SOFSEM, CiE, ....)
23 Ph D students,
Examinator of 1000 students math, CS, Logic, AI, ...
Peter van Emde Boas:
Victorious Warriors 20140507
Topics
• Introduction: the project “History of Logic in China”
• Theory of strategy: then and now
• Ancient Chinese Strategy theory as described by
Sun Tzu
– There is logic in these ancient texts
• Example stories related to games from the
Romance of the Three Kingdoms
–
–
–
–
–
Lü Bu and Diao Chan
Jian Gan steals a letter
Cao Cao divides Han Suo and Ma Chao
Zhuge Liang borrows arrows
The ambush at Huarong
Peter van Emde Boas:
Victorious Warriors 20140507
A Wild Idea
Fenrong Liu
Analyze Classical Chinese
Strategy Theory from the
Perspective of contemporary
Game Theory ??!
Jeremy Seligman
Peter van Emde Boas:
Victorious Warriors 20140507
Jun 07 2012
The Project
• Preparation for the handbook of the history of logic
in China (the meeting at Nankai University in April
2014)
• A proposed chapter in this handbook, including
topics like:
– Ancient Chinese theory of Military Strategy: Sun Tzu and
Sun Bin
– Connections to Logic, and Game Theory
– Example stories from history and/or litterature such as the
three kingdoms saga
– Contemporary perspective
• This presentation is about issues inspired by this
project and has a wider perspective
– The problems of reconstructing games from stories
Peter van Emde Boas:
Victorious Warriors 20140507
Join me on a trip to Ancient China
Great Wall Wonder Movie in Civilization II
Great Wall Wonder Movie in Civilization IV
Peter van Emde Boas:
Victorious Warriors 20140507
My first encounter with Sun Tzu
Sun Tzu War Academy Wonder Movie in Civilization II
Peter van Emde Boas:
Victorious Warriors 20140507
My first encounter with the three
Kingdoms saga
During my trip to Guanzhou in
2009 I saw the two part version
of this movie during the flights
In Europe the reduced single part
edition is regularly broadcasted
on TV
Peter van Emde Boas:
Victorious Warriors 20140507
Another source of inspiration
Yanjing Wang, ph.d. thesis ILLC, 20100921,
Epistemic Modelling & Protocol Dynamics, ch 1
Peter van Emde Boas:
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The PhD defense of Yanjing Wang
© Peter van Emde Boas ; 20100921
It was a great event……
© Peter van Emde Boas ; 20100921
Peter van Emde Boas:
Victorious Warriors 20140507
So I started reading….
Peter van Emde Boas:
Victorious Warriors 20140507
Timeline of historic events
771 – 476 BC
551 – 479 BC
Around 500 BC
476 – 221 BC
Around 360 BC
221 – 207 BC
206 BC – 220 AD
168 – 280
265 – 420
1206 – 1386
Around 1370
1386 – 1644
1522
1644 – 1911
1911 – today
Spring and Autumn Period
Confucius
Sun Wu
Warring States Period
Sun Bin
Qin Dynasty
Han Dynasty
Romance Three Kingdoms period
Jin Dynasty
….
Yuan Dynasty
Presumed writing of the Three Kingdoms
Ming Dynasty
Printed edition Three Kingdoms
Qing Dynasty
Revolution, Civil War, Japanese Occupation,
Peoples Republic
Peter van Emde Boas:
Victorious Warriors 20140507
Some Source Texts
Sun Tzu
Sun Bin
The Art of War
The Art of War
Romance of the Three Kingdoms
around 500 BC
around 360 BC
around 1400 AD
The 13 chapters in Sun Tzu, the Art of War
1
2
3
4
5
6
7
Strategic Assessments
Doing Battle
Planning a Siege
Formation
Force
Emptiness and Fullness
Armed Struggle
8 Adaptations
9 Maneuvring Armies
10 Terrain
11 Nine Grounds
12 Fire Attack
13 On the use of Spies
Peter van Emde Boas:
Victorious Warriors 20140507
The Authors
Peter van Emde Boas:
Victorious Warriors 20140507
The Sources
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Victorious Warriors 20140507
Replica of Sun Tzu text in National Museum Beijing
Peter van Emde Boas:
Victorious Warriors 20140507
Translations/Editions
Consider my favourite Sun Tzu quote:
Victorious Warriors win first and then go to War,
while Defeated Warriors go to War first and then seek to win.
Did Sun Tzu actually say/write this? if so, where?
Phrases like this appear both at the end of the first chapter
(Strategic Assessments) and in chapter four (Formation)
Peter van Emde Boas:
Victorious Warriors 20140507
Wu Rusong ch4
Cleary ch4
John Minford ch4
Cleary ch1
Cleary ch4
Sawyer ch4
Ames ch 4
Here it appears
Cleary ch1
Peter van Emde Boas:
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Logic, Games and Ancient Strategy
Peter van Emde Boas:
Victorious Warriors 20140507
Where is the Logic?
• Sun Tzu and Sun Bin express their advice
in terms of rules
– Using rules means using logic
• Information, knowledge and belief are core
concepts in their strategic theory
– These concepts are studied using logic
From the ILLC mission statement:
The scientific mission of the Institute for Logic, Language and
Computation (ILLC) is to study formal properties of information,
viz. the logical structure and algorithmic properties of
processes of encoding, transmitting and comprehending information.
Peter van Emde Boas:
Victorious Warriors 20140507
Semi-structured text
Sun Tzu, ed. Wu Rusong, ch 11
Rules
Definitions
Sun Tzu, ed. Wu Rusong, ch 11
Peter van Emde Boas:
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The definitions in this example text
1.
2.
3.
4.
5.
6.
7.
8.
9.
San, Dispersive, Within one’s own state
Qing, Marginal, Enemy territory (short distance)
Zheng, Contested, Advantageous for first occupant
Jiao, Open, Accessible to both sides
Qu, Focal, Border area of several states
Zhong, Critical, Deep in enemy territory
Pi, Difficult, Mountains, forests and other natural hazards
Wei, Beleaguered, Narrow and tortuous entrances
Si, Deadly, Survival is very hard
Peter van Emde Boas:
Victorious Warriors 20140507
The rules in this example text
1.
2.
3.
4.
5.
6.
7.
8.
9.
Do not fight in dispersive region
Do not linger in a marginal region
Do not strain to attack the enemy in contested region
Do no get cut off in an open region
Form alliances in focal region
Plunder the enemy’s resources in critical region
Press ahead in a difficult region
Devise contingency plans in a beleaguered region
Fight with all courage and energy in a deadly region
Peter van Emde Boas:
Victorious Warriors 20140507
Where is the Game Theory?
• Game theory is a mathematical theory aimed
at the description of behavior of opponents
(agents) in strategic interaction
• This is what the ancient Chinese strategy
thinkers were doing also, except for the
missing Mathematics…
– Linear algebra, probability theory,…
• The Game theoretical ingredients can be
found primarily in the historical stories
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About these connections
• The texts of Sun Tzu and Sun Bin were almost
unknown in the Western world before 1950
• Interesting modern ideas can be found in these
texts (and histories) which are 2500 years old.
– Analyzing the situation
– Information
– Theory of mind reasoning (E.G. in the three kingdoms
stories)
• These modern ideas play a role in Game Theory
Peter van Emde Boas:
Victorious Warriors 20140507
Analyzing the situation
Military Tradition Splash screen in Civilization IV
Peter van Emde Boas:
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Analyzing the situation
Victorious warriors win first and then go to war, while defeated
warriors go to war first and then seek to win
Sun Tzu, the Art of War
This phrase invites to analyze the situation before engaging
in battle.
Is this a form of game analysis?
Did the ancient Chinese actually use such an analysis?
If so, can we find evidence for this in ancient texts?
Peter van Emde Boas:
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Information and Spies
An expendable agent is one who
is deliberately given false information
to mislead the enemy
Information is mentioned as a
transferable entity
This is around 500 BC
Wu Rusong ch13
Peter van Emde Boas:
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Theory of mind reasoning
• Ambush at Huarong
– See the quotation by Yanjing Wang
– Presented in more details later
– Believed to be fictitious
• Empty City strategy
– Strategy 32 in the 36 strategies
– Famous example by Zhuge Liang in the three
kingdoms saga (believed to be historical rather
than fictitious)
Peter van Emde Boas:
Victorious Warriors 20140507
Some other Sun Tzu Quotes
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Be prepared
The art of war teaches us to rely not on the likelihood of
the enemy’s not attacking, but rather on the fact that we
have made our position unassailable.
Great Wall wonder Splash screen quote from Sun-Tzu in Civilization V
Sun Tzu, ed. Wu Rusong, ch8
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Victorious Warriors 20140507
Know thy Enemy
Sun Tzu, ed. Clarey, ch3
Peter van Emde Boas:
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Deception is everything
If he is united as one, divide him
Divide et Impera
(divide and conquer)
Sun Tzu, the Art of War, ch 1; ed. Wu Rusong
Peter van Emde Boas:
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Divide et Impera in Roman History
Peter van Emde Boas:
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Strategic Theory, then and now
Peter van Emde Boas:
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Theory of Military Strategy
This text was written in 1832
Start of Strategic Theory ??
Peter van Emde Boas:
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Sun Tzu, the Art of War
This text was written around 500 BC
Peter van Emde Boas:
Victorious Warriors 20140507
The changed nature of War
Guandu 200 AD
Solferino 1859; national armies
Normandy 1944; mechanisation
Syria today; insurgents
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Victorious Warriors 20140507
The ultimate game changer
Hiroshima 1945
War is no longer a constant-sum game; It is no longer
clear which actions of policy makers are rational.
Anatol Rapoport
Peter van Emde Boas:
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Classic perspective
•
Mercenary armies
•
•
•
•
•
•
Soldiers fight for who pays, feeds or
owns them
Observe Warriors code of honour
Commanders participate in combat
Defeat the enemy; don’t destroy him
Prevent casualties, if possible
If defeated, you may switch side
The Chinese ancient strategy
theoreticians must be understood
from this classic perspective
Is this correct ?
Alexanderschlacht, Alex Altdorfer
Alte Pinakotek, Műnchen
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Commanders in combat
Beijing, Summer palace, long corridor;
the nightly combat between Ma Chao and Zhang Fei
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Compare with von Clausewitz
Peter van Emde Boas:
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Compare with von Clausewitz
• The idea that you can overcome the
enemy using strategy only, without
serious fighting is a severe error
• Stratagems are to be used as a last
resort only
Chinese advocate deception in all circumstances;
For a last resource advice look at Strategy 36 from the
36 strategies of ancient China
If nothing else works, retreat
Peter van Emde Boas:
Victorious Warriors 20140507
Stories and games
Peter van Emde Boas:
Victorious Warriors 20140507
Analyzing texts
• We learn about ancient Chinese events
from history texts and literature
• These sources provide us with Stories
• We read about the use of Stratagems in
these stories (tricks of deceit during
warfare)
• What does this tell about the actual
strategic situation? About the Games
involved?
Peter van Emde Boas:
Victorious Warriors 20140507
The Oberver from Mars problem
How much can the Martian Observer learn about the Go Game
by observing a (single) play performed by human players?
Peter van Emde Boas:
Victorious Warriors 20140507
Reconstructing Games from Stories
From a given story, invent some plausible game so that the story
becomes a play in the game.
This makes it possible to appreciate the behavior of the agents
in the story
Were they rational, wise, sensitive, compassionate, …?
And did they use any kind of game analysis at all?
Peter van Emde Boas:
Victorious Warriors 20140507
A possible approach: Narratology
• A form of literature study, aimed at constructing
formal representations of the content of stories
• Primary target: a sequence of events
• But that’s not all
–
–
–
–
What did agents knew?
What did agents believe?
What did agents desire?
What did agents expect?
• Are two stories similar or equivalent?
• Are the stories instances of similar or equivalent
games?
• It is a non-trivial task!
• So far we did not attempt to use this approach for
our Chinese texts
Peter van Emde Boas:
Victorious Warriors 20140507
Example of Narratology study
Higher order theory-of-mind representation of preferences
and/or expectations of agents participating in the stories.
Example stories from popular TV crime series
Peter van Emde Boas:
Victorious Warriors 20140507
Example stories
• Lu Bu and Dian Chao
– Reconstruction of game from story
• Jian Gan steals a letter
– Information; the expendable spy
• Cao Cao divides Ma Chao and Han Suo
– Information; non-information works also
• Zhuge Liang borrow arrows
– Multiple games played simultaneously
• The ambush at Huarong
– Theory-of-mind reasoning
Peter van Emde Boas:
Victorious Warriors 20140507
Lü Bu and Diao Chan
Used as an example for strategy 31 (Strategy of the beautiful women)
in my edition of the thirty-six strategies of Ancient China
Peter van Emde Boas:
Victorious Warriors 20140507
Set-up of the story
Dong Zhuo, after the gang of ten Eunuchs who have corrupted
the court has been eliminated, is usurping power in the late Han empire.
He obtains the service of Lü Bu, a fierce and invincible warrior, to
protect him.
Dong Zhuo disposes the ruling emperor Ling and has him replaced by
his weaker and younger brother Xian. The former emperor Ling is killed.
Dong Zhuo behaves more and more as a Tyrant.
Minister of the interior Wang Yun sees more and more heads rolling
around him, and fears his head will be next on the block.
Together with Diao Chan – a beautiful girl in his household, Wang Yun
designs a plot to destroy the good relation between Dong Zhuo and
Lü Bu.
Peter van Emde Boas:
Victorious Warriors 20140507
Wang Yun and Dioa Chan forge a plot to separate Lü Bu and
Dong Zhuo
Peter van Emde Boas:
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The story of Lü Bu and Diao Chan
Wang Yung invites Lü Bu for dinner; offers him Diao Chan as bride
Wang Yung invites Dong Zhuo for dinner; offers him Diao Chan as concubine
Observing Diao Chan in the palace of Dong Zhuo, Lü Bu asks Wang Yung for
explanation; he tells that Dong Zhuo obtained Diao Chan by political pressure
Lü Bu meets Diao Chan in the palace garden; she confirms Wang Yung story
Dong Zhuo observes this meeting; Diao Chan tells him that Lü Bu attempted
to seduce her
The plot succeeds; Dong Zhuo and Lu Bü become enemies.
Later Lü Bu will kill Dong Zhuo and marry Diao Chan
Peter van Emde Boas:
Victorious Warriors 20140507
What is the Game?
The story introduces four agents, and a sequence of events.
Which events offer a choice point where a strategic move is made?
What would be the alternative moves at such a position?
The story involves lies; hence ascribing belief states to agents is
essential for really understanding what happens. (but we have not
yet done it)
What about preferences and/or utilities?
Peter van Emde Boas:
Victorious Warriors 20140507
Events in a possible model
Offer as bride
Offer as concubine
Observation by Lü Bu
Lies by Wang Chun and
Diao Chan
Which choices are open for
other agents?
Observation by Dong Zhuo
Lie by Diao Chan
Plot Succeeds
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Offer as bride
Accept offer?
Y
N
Y
N
Offer as concubine
Accept offer?
Disregard?
Observation by Lü Bu
Lies by Wang Chun and
Diao Chan
N
Y
Y
N
Believe lies?
Observation by Dong Zhuo
N
Y
Y
N
Disregard?
Lie by Diao Chan
Believe lie?
Plot Succeeds
Possible Choice Points added
Peter van Emde Boas:
Victorious Warriors 20140507
Offer as bride
Accept offer?
[???0]
Y
N
Y
N
Offer as concubine
Accept offer?
Observation by Lü Bu
[?++?]
[---+]
N
Y
Disregard?
Lies by Wang Chun and
Diao Chan
[---+]
Believe lies?
Y
N
N
Y
Y
N
Observation by Dong Zhuo
[?--?]
Disregard?
Lie by Diao Chan
Believe lie?
[?--?]
Plot Succeeds
[ + + + 1/2 ]
Peter van Emde Boas:
Victorious Warriors 20140507
Utilities ?
Jian Gan steals a letter
Example of the use of information; the expendable spy strategy
Peter van Emde Boas:
Victorious Warriors 20140507
Jian Gan steals a letter
Cao Cao sends an secret envoy, Jiang Gan, to Zhou Yu (the enemy
commander), in order to convince the latter to surrender.
Zhou Yu, recognizes that it is a spy, but receives and feasts him
like an old friend. During the night he arranges that Jian Gan finds
a secret letter, written by the two admirals of Cao Cao, indicating
that they intend to defect to Zhou Yu. Jiang Gan steals the letter.
Upon return Jiang Gan informs Cao Cao about his findings; the two
admirals are beheaded.
However, the letter was a planted forgery; the admirals were innocent,
and Cao Cao realises that he has been tricked only after the execution.
Romance of the three Kingdoms, chapter 45
Peter van Emde Boas:
Victorious Warriors 20140507
This example is an instance of the
expendable agent strategy
An expendable agent is one who
is deliberately given false information
to mislead the enemy
Sun Tzu, the Art of War, Wu Rusong ch13
Peter van Emde Boas:
Victorious Warriors 20140507
Cao Cao divides Han Suo and Ma Chao
Example of use of non-information
After his defeat at Red Cliffs (208), the attempts of Cao Cao to extend the
territory he controls to the south come to halt. A few years later he attempts to
get the Northwest regions under his control (211).
His first opponent there is Han Sui, who is served by his nephew Ma Chao.
Earlier Cao Cao has killed the father of Ma Chao and two of his brothers.
Initially Cao Cao had tried to convince Han Sui to surrender and to deliver Ma Chao
to him, but Han Sui refused. Han Sui goes to war against Cao Cao, but at
Tong Pass, after some initial victories by Ma Chao, the two armies get stuck in a
stalemate. Winter is arriving and the two parties start negotiating a truce.
Seeing no way to defeat Ma Chao, Cao Cao designs a plot to create division
between Ma Chao and Han Sui.
Romance of the three Kingdoms, chapt 59
Peter van Emde Boas:
Victorious Warriors 20140507
Cao Cao’s plot
In between battles Cao Cao has a discussion with Han Sui;
they discuss in public old events rather than the actual status.
Cao Cao sends a letter to Han Sui filled with erasures; asked for an
explanation by Ma Chao, Han Sui can’t explain why Cao Cao has produced
such a sloppy contentless document.
Cao Cao and Han Sui, have another discussion at the battle field, where
Cao Cao expresses thanks for the earlier words of Han Sui.
These developments make Ma Chao more and more suspicious, and Han Sui
feels it. Subsequently he figures out that defecting to Cao Cao is after all
the wisest policy at this stage. However his intentions to defect to Cao Cao
and organize an murder attempt on Ma Chao become known to Ma Chao.
Ma Chao attempts a preemptive strike on Han Sui, who is saved by Cao Cao,
and Ma Chao narrowly escapes. Cao Cao is now victorious at Tong Pass.
Romance of the three Kingdoms, chapt 59
Peter van Emde Boas:
Victorious Warriors 20140507
Romance of the three Kingdoms, chapt 59
Peter van Emde Boas:
Victorious Warriors 20140507
Use of non-information
• Cao Cao divides Han Suo and Ma
Chao by creating the impression that
he exchanges secret information
with Han Suo
• But in reality nothing is exchanged
• Still Ma Chao is convinced that a plot
against him is designed and attacks
Han Suo as a preemptive strike
Peter van Emde Boas:
Victorious Warriors 20140507
Hear the commentary
Peter van Emde Boas:
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The commentaries
• The first comment expresses how
ingeniously Cao Cao succeeds in making
Ma Chao suspicious
• The second comment states that the key
difference is that in this example the
exchange of information is public,
contrary to the Jian Gan example, where
the communication is secret
• I see yet another important difference:
information vs. non information
Peter van Emde Boas:
Victorious Warriors 20140507
Borrowing Arrows
Two games being played simultaneously
Peter van Emde Boas:
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Zhuge Liang (Kongming) borrows arrows
Kongming plays and wins two games
at the same time:
-- Strategem against Cao Cao
-- Saves himself from Zhou Yu’s plot
Before the battle at Red Cliffs (208 AD)
Zhou Yu assigns to Kongming (Zhuge Liang)
the “mission impossible” task of procuring
100 000 arrows.
Kongming assembles a small fleet of 20 ships
covered by straw and feigns an attack at
Cao Cao on the opposite side of the river
at dawn in the fog. Cao Cao’s troops are
deceived and fire more than 150 000 arrows
which are well preserved in the straw, and
collected.
Romance of the three Kingdoms, Chapter 46
Peter van Emde Boas:
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Archery Splash screen in Civilization IV
Peter van Emde Boas:
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The ambush at Huarong
Peter van Emde Boas:
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The ambush at Huarong
• Cao Cao is retreating from the defeat at Red Cliffs
• He must take the mountain road or the road
through the valley
• His scouts inform him that there are fires lit along
the mountain road
• Cao Cao, believing that the fires are intended to
deceive him into taking the valley road, decides
to take the mountain path
• But the ambush actually is located along the
mountain road, since Zhuge Liang predicted how
Cao Cao would reason
Peter van Emde Boas:
Victorious Warriors 20140507
The formal representation
E
W
E
-1/1 1/-1
W
1/-1 -1/1
Cao Cao does not want to be ambushed
He can take the valley or the mountain road
Lord Guo can stage the ambush in the valley of the montain road
If both warriors select the same location Lord Guo wins;
otherwise Cao Cao escapes
This game is known as the game of matching pennies in Game Theory
Peter van Emde Boas:
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Ambush at Huarong
• As a game it is just Matching Pennies
• Actually Zhuge Liang may loose the game, by
moving first (exposing his position)
• Cao Cao uses second order theory-of-mind
reasoning
– Reasoning about what Zhuge Liang could reason
• Zhuge Liang uses third order theory-of-mind
reasoning
– Reasoning about what Cao Cao could reason about
what Zhuge Liang could reason
• Therefore Zhuge Liang wins
Peter van Emde Boas:
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Cao Cao’s reasonings
Cao Cao refers to
Sun Tzu
Romance of the three Kingdoms, ch 50
Peter van Emde Boas:
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Zhuge Liang’s reasoning
Zhuge Liang
Predicts that
Cao Cao will refer to
Sun Tzu
Romance of the three Kingdoms, ch 49
Peter van Emde Boas:
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What are they talking about
Appear to be far away when actually
nearby, and vice versa
This story includes a direct
reference to the teachings
of Sun Tzu
Sun Tzu, the Art of War, ch 1; ed. Wu Rusong
Peter van Emde Boas:
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Cao Cao escapes
Cao Cao actually is ambushed three consecutive times during his
retreat after the battle at Red Cliffs. At Huarong he is granted
free passage by the local commander Lord Guan
Romance of the three Kingdoms, ch 50
Is the cliffhanger a Chinese Invention ??
Peter van Emde Boas:
Victorious Warriors 20140507
Hear the commentator
Peter van Emde Boas:
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Again Zhuge Liang is playing two
games at the same time
• Before assigning the final ambush to
Lord Guan, Zhuge Liang has predicted
that Lord Guan will let Cao Cao escape
• This is essential for the future
– His lord Liu Bei is not yet ready to cope
with his “ally” Sun Quan and his general
Zhou Yu
– Therefore Cao Cao should not yet be
eliminated
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Zhuge Liang predicts the outcome
Guan Yu puts his head
at stake
Romance of the three Kingdoms, ch 49
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Why I like this story?
• Use of third order theory-of-mind
reasoning
– Do you know of other examples ?
• Explicit reference to the teachings of
the Ancient Chinese theoreticians of
strategy
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Concluding remarks
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Reconstructing games from stories?
• Martian observer’s problem
– We only have one game play available
• Several games played in parallel
– Fusing several games into a big game creates
problems of preference aggregation
• Do we get games at all?
– The assumption of common knowledge of the
game may be violated
– The agents may have (false) beliefs on the
preferences of others
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Loose Ends
• Many more texts remain to be studied
(seven classics)
• Are there more stories involving higher
theory-of-mind reasoning?
• What happened inbetween 500 BC and
1832?
• Did the Chinese learn to prepare for the
tricks of their opponents?
• What was done outside China?
– Roman authors?
Peter van Emde Boas:
Victorious Warriors 20140507
Romance of the three Kingdoms, ch 1
Romance of the three Kingdoms, ch 120
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The end
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Victorious Warriors 20140507