peter van emde boas: victorious warriors 20140507 victorious warriors peter van emde boas,...

Peter van Emde Boas: Victorious Warriors 20140507

Victorious WarriorsPeter van Emde Boas, ILLC-FNWI-UvA and

Bronstee.com Software & Services B.V.

20140507

Peking University

Logic in Sun Tzu and the

Games playedin the Romance

of the ThreeKingdoms


Who am I ?Born: 19450403 ( 4 years before foundation PRC)MS & PhD: University of Amsterdamsupervisors: van Wijngaarden, Baayen, Hartmanis (Turing Award winner)Fields: Mathematics, Computer Science, Logic50 years of professional activity-- van Emde Boas Priority QueueLong term involvement with mayor Conference series (ICALP, TAMC, SOFSEM, CiE, ....)23 Ph D students, Examinator of 1000 students math, CS, Logic, AI, ...


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


A Wild Idea

Jun 07 2012

Analyze Classical Chinese Strategy Theory from thePerspective of contemporaryGame Theory ??!

Fenrong Liu

Jeremy Seligman


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


Join me on a trip to Ancient China

Great Wall Wonder Movie in Civilization II Great Wall Wonder Movie in Civilization IV


My first encounter with Sun Tzu

Sun Tzu War Academy Wonder Movie in Civilization II


My first encounter with the three Kingdoms saga

During my trip to Guanzhou in2009 I saw the two part versionof this movie during the flights

In Europe the reduced single partedition is regularly broadcastedon TV


Another source of inspiration

Yanjing Wang, ph.d. thesis ILLC, 20100921,Epistemic Modelling & Protocol Dynamics, ch 1


It was a great event……

© Peter van Emde Boas ; 20100921

© Peter van Emde Boas ; 20100921

The PhD defense of Yanjing Wang


So I started reading….


Timeline of historic events771 – 476 BC Spring and Autumn Period551 – 479 BC ConfuciusAround 500 BC Sun Wu476 – 221 BC Warring States PeriodAround 360 BC Sun Bin221 – 207 BC Qin Dynasty206 BC – 220 AD Han Dynasty168 – 280 Romance Three Kingdoms period265 – 420 Jin Dynasty

….1206 – 1386 Yuan DynastyAround 1370 Presumed writing of the Three Kingdoms1386 – 1644 Ming Dynasty1522 Printed edition Three Kingdoms1644 – 1911 Qing Dynasty1911 – today Revolution, Civil War, Japanese Occupation,

Peoples Republic


Some Source Texts

Sun Tzu The Art of War around 500 BCSun Bin The Art of War around 360 BC

Romance of the Three Kingdoms around 1400 AD

The 13 chapters in Sun Tzu, the Art of War

1 Strategic Assessments 8 Adaptations2 Doing Battle 9 Maneuvring Armies3 Planning a Siege 10 Terrain4 Formation 11 Nine Grounds5 Force 12 Fire Attack6 Emptiness and Fullness 13 On the use of Spies7 Armed Struggle


The Authors


The Sources


Replica of Sun Tzu text in National Museum Beijing


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)


Wu Rusong ch4

John Minford ch4

Cleary ch1

Cleary ch4

Cleary ch1

Cleary ch4

Sawyer ch4

Ames ch 4

Here it appears


Logic, Games and Ancient Strategy


Where is the 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.

• 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


Semi-structured text

Definitions

Rules

Sun Tzu, ed. Wu Rusong, ch 11

Sun Tzu, ed. Wu Rusong, ch 11


The definitions in this example text

1. San, Dispersive, Within one’s own state2. Qing, Marginal, Enemy territory (short distance)3. Zheng, Contested, Advantageous for first occupant4. Jiao, Open, Accessible to both sides5. Qu, Focal, Border area of several states6. Zhong, Critical, Deep in enemy territory7. Pi, Difficult, Mountains, forests and other natural hazards8. Wei, Beleaguered, Narrow and tortuous entrances9. Si, Deadly, Survival is very hard


The rules in this example text

1. Do not fight in dispersive region

2. Do not linger in a marginal region

3. Do not strain to attack the enemy in contested region

4. Do no get cut off in an open region

5. Form alliances in focal region

6. Plunder the enemy’s resources in critical region

7. Press ahead in a difficult region

8. Devise contingency plans in a beleaguered region

9. Fight with all courage and energy in a deadly region


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


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


Analyzing the situation

Military Tradition Splash screen in Civilization IV


Analyzing the situation

Victorious warriors win first and then go to war, while defeatedVictorious warriors win first and then go to war, while defeated warriors go to war first and then seek to winwarriors go to war first and then seek to win

Sun Tzu, the Art of WarSun 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?


Information and Spies

Wu Rusong ch13

Information is mentioned as a transferable entity

This is around 500 BC

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


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)


Some other Sun Tzu Quotes


Be prepared

Sun Tzu, ed. Wu Rusong, ch8

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


Know thy Enemy

Sun Tzu, ed. Clarey, ch3


Deception is everything

Sun Tzu, the Art of War, ch 1; ed. Wu Rusong

Divide et Impera(divide and conquer)

If he is united as one, divide him


Divide et Impera in Roman History


Strategic Theory, then and now


Theory of Military Strategy

This text was written in 1832

Start of Strategic Theory ??


Sun Tzu, the Art of War

This text was written around 500 BC


The changed nature of War

Guandu 200 AD Solferino 1859; national armies

Normandy 1944; mechanisation Syria today; insurgents


Hiroshima 1945

War is no longer a constant-sum game; It is no longer clear which actions of policy makers are rational.Anatol Rapoport

The ultimate game changer


Classic perspective

Alexanderschlacht, Alex AltdorferAlte Pinakotek, Műnchen

• 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 ?


Commanders in combat

Beijing, Summer palace, long corridor; the nightly combat between Ma Chao and Zhang Fei


Compare with von Clausewitz


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 onlyChinese 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


Stories and games


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?


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?


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?


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


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


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


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


Dong Zhuo, after the gang of ten Eunuchs who have corruptedthe court has been eliminated, is usurping power in the late Han empire.

He obtains the service of Lü Bu, a fierce and invincible warrior, toprotect 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 Yundesigns a plot to destroy the good relation between Dong Zhuo andLü Bu.

Set-up of the story


Wang Yun and Dioa Chan forge a plot to separate Lü Bu and Dong Zhuo


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 attemptedto seduce her

The plot succeeds; Dong Zhuo and Lu Bü become enemies.

Later Lü Bu will kill Dong Zhuo and marry Diao Chan


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 isessential for really understanding what happens. (but we have not yet done it)

What about preferences and/or utilities?


Events in a possible modelOffer as bride

Offer as concubine

Lies by Wang Chun and Diao Chan

Lie by Diao Chan

Observation by Lü Bu

Observation by Dong Zhuo

Plot Succeeds

Which choices are open for other agents?


Offer as bride

Offer as concubine

Lie by Diao Chan



Plot Succeeds

Accept offer?

Accept offer?

Believe lies?

Believe lie?

Disregard?

Disregard?

Possible Choice Points added


Y N

N

N

Y

Y

N

Y

N

Y

N

Y


Offer as bride

Offer as concubine

Lie by Diao Chan



Plot Succeeds

Accept offer?

Accept offer?

Believe lies?

Believe lie?

Disregard?

Disregard?

Utilities ?


[ + + + 1/2 ]

[ ? - - ? ]

[ ? ? ? 0 ]Y N

N

N

Y

Y

N

Y

N

Y

N

Y

[ ? + + ? ]

[ - - - + ]

[ - - - + ]

[ ? - - ? ]


Jian Gan steals a letter

Example of the use of information; the expendable spy strategy


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 findsa secret letter, written by the two admirals of Cao Cao, indicatingthat they intend to defect to Zhou Yu. Jiang Gan steals the letter.

Upon return Jiang Gan informs Cao Cao about his findings; the twoadmirals 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


This example is an instance of the expendable agent strategy

Sun Tzu, the Art of War, Wu Rusong ch13

An expendable agent is one who is deliberately given false information to mislead the enemy


Cao Cao divides Han Suo and Ma Chao

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

Example of use of non-information


Cao Cao’s plotIn 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 anexplanation by Ma Chao, Han Sui can’t explain why Cao Cao has producedsuch a sloppy contentless document.

Cao Cao and Han Sui, have another discussion at the battle field, whereCao Cao expresses thanks for the earlier words of Han Sui.

These developments make Ma Chao more and more suspicious, and Han Suifeels it. Subsequently he figures out that defecting to Cao Cao is after allthe wisest policy at this stage. However his intentions to defect to Cao Caoand 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.



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


Hear the commentary


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


Borrowing Arrows

Two games being played simultaneously


Zhuge Liang (Kongming) borrows arrows

Before the battle at Red Cliffs (208 AD)Zhou Yu assigns to Kongming (Zhuge Liang)the “mission impossible” task of procuring100 000 arrows.

Kongming assembles a small fleet of 20 shipscovered by straw and feigns an attack atCao Cao on the opposite side of the riverat dawn in the fog. Cao Cao’s troops aredeceived and fire more than 150 000 arrowswhich are well preserved in the straw, andcollected.

Kongming plays and wins two games at the same time:-- Strategem against Cao Cao-- Saves himself from Zhou Yu’s plot

Romance of the three Kingdoms, Chapter 46


Archery Splash screen in Civilization IV


The ambush at Huarong


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


The formal representation

E

W

E W

1/-1

1/-1

-1/1

-1/1

Cao Cao does not want to be ambushedHe can take the valley or the mountain roadLord 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


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


Romance of the three Kingdoms, ch 50

Cao Cao’s reasonings

Cao Cao refers toSun Tzu



Zhuge Liang’s reasoning

Zhuge LiangPredicts thatCao Cao will refer toSun Tzu


What are they talking about

Sun Tzu, the Art of War, ch 1; ed. Wu Rusong

This story includes a direct reference to the teachings of Sun Tzu

Appear to be far away when actually nearby, and vice versa


Cao Cao escapesCao 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

Is the cliffhanger a Chinese Invention ??



Hear the commentator


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


Zhuge Liang predicts the outcome


Guan Yu puts his headat stake


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


Concluding remarks


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


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?


Romance of the three Kingdoms, ch 1 Romance of the three Kingdoms, ch 120


The end

peter van emde boas: victorious warriors 20140507 victorious warriors peter van emde boas,...

Documents

van wijngaarden

huarong slide

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project history of logic

china theory of strategy

peking university logic

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