peter van emde boas: reconstructing games from stories lorentz center, leiden, 20150626...

Peter van Emde Boas: Reconstructing games from storiesLorentz Center, Leiden, 20150626

Reconstructing games from storieswhy we should want to do it and why it will be hard to do so

20150626

Peter van Emde Boas, ILLC-FNWI-UvA andBronstee.com Software & Services B.V.

Workshop Clusters, Games and Axioms(previously presented at CiE 2014 – Budapest)


Topics

• Origin of the problem– A rather unusual inference problem

• Reasons why it is hard to solve• What does this tell us about shortcomings of

game theory


The Project

• Preparation for the handbook of the history of logic in China

• (History of Logic in China III meeting at Nankai University; April 2014)

• My contribution is a chapter in this handbook: – Ancient Chinese theory of Military Strategy: Sun Tzu and

Sun Bin– Connections to Logic, and Game Theory– Contemporary perspective

• This presentation is about an issue inspired by this project: – Determine whether the Ancient Chinese Warlords actually

did use the strategic guidelines proposed by their masters


Sources used


SourcesSun Tzu The Art of War around 500 BC

Romance of the Three Kingdoms around 1400 ADdescribing events during the period 168 – 260 AD (A period ofCivil war leading to the end of the Han Dynasty)

The 13 chapters in the classic Sun Tzu 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


Motivating QuoteVictorious 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.

Did the ancient Chinese actually use such an Analysis?

What could the Chinese have analyzed in a concrete situation?


A fundamental problem

• How to research these questions?• We find in historical texts and literature examples

of actual battles in Ancient China• These texts provide us with Stories• We read about the use of Stratagems in these

stories– Stratagem: trick or deceit during warfare

• What does this tell about the actual strategic situation?

• How can we model this strategic situation in terms of a Game?


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 opponents in the story

Were they rational, wise, sensitive, compassionate, …?


A related field: 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 opponents know?– What did opponents believe?– What did opponents desire?– What did opponents expect?

• It is a non-trivial task!


Narratology and games

• When are two stories similar or equivalent?– This has been studied

• Are two stories instances of similar or equivalent Games / Strategic Contexts?– This could be a new question


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


A key observation in this study

• Agents may have false beliefs about the expectations and preferences of other agents

• These false beliefs are essential for understanding the events in the story

• This violates a basic assumption in Game theory: the assumption that the agents have common knowledge of the game– This common knowledge includes the

preferences of the agents


The Martian Observer’s problem

How much can the Martian Observer learn about the Go Game by observing a (single) play performed by human players?


Joseph and the wife of Potifar

• Story from Genesis 39; first book in the Bible, old testament

• Joseph is sold by his jealous brothers in slavery

• He arrives in Egypt where he becomes slave and housemaster of lord Potifar

• Potifars wife makes several attempts to seduce Joseph; they all fail.


Story in the Bible

Potifar’s wife, being alone with Joseph, makes another attempt having lured Joseph into her bedroom

Joseph again refuses and wants to escape; but he looses part of his cloth

Wife accuses Joseph of an attempted rape

Potifar believes wife

Joseph is send to prison


Story in the Qu’ran (Soura 12, 23-36)

Potifar’s wife, being alone with Joseph, makes another attempt having lured Joseph into her bedroom

Joseph again refuses and wants to escape; but he looses part of his cloth

Wife accuses Joseph of an attempted rape

Joseph defends himself; a clever witness presents evidence of his innocence ( from which side the cloth was torn ? )

Potifar does not believes his wife

Joseph is acquitted (initially)

and then something strange happens

Joseph is taken into protective custody

An alternative storyline involving a choice point unmentioned in the Bible


Example: the ambush at Huarong

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


Example: 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, staged by Lord Guan, actually is located along the mountain road, since Zhuge Liang (Kongming) predicted how Cao Cao would reason


The formal representation

V

M

V M

1/-1

1/-1

-1/1

-1/1

Cao Cao does not want to be ambushedHe can take the Valley or the Mountain roadLord Guan can stage the ambush in the Valley of the Montain road

If both warriors select the same location Lord Guan and Zhuge Liang win; 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 (Kongming) 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

• Both warlords actually invoke Sun Tzu’s teachings in motivating their choices

• Beware: this story is believed to be fictitional rather than historical


What Sun Tzu teaches

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

The concept of Deception involved is mentionedin Sun Tzu. But no higher order Theory-of-mind reasoning.

The story actually involves third Order Theory-of-mind Reasoning;


Reconstructing games from stories?

• Martian observer’s problem– We only have one game play available

• 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

• Several games played in parallel– Fusing several games into a big game creates

problems of preference aggregation


Actually Zhuge Liang is playing two games at the same time

• Zhuge Liang assigns the task for staging the ambush to Lord Guan

• Before assigning the final ambush to Lord Guan, Zhuge Liang has predicted that Lord Guan humilate Cao Cao but also will let Cao Cao escape

• This is essential for the sequel of the civil war– 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 removed from the

game


Playing simultaneous games

• Is this not just a matter of merging several games into a bigger game?

• Game theory provides several mechanisms for combining games

• OK with respect to positions and moves

• Preference aggregation becomes now a problem.


Are Games Adequate?

• Game Theory is said to be a theory about agents in strategic interaction

• This should include Military interaction as well

• In real life however, basic assumptions from Game Theory are not satisfied E.G., Common Knowledge of the game amongst the players


The end


Some Sun Tzu quotes

Wu Rusong ch8

Clarey ch3


Romance of the three Kingdoms, ch 50

Cao Cao’s reasonings



Zhuge Liang’s resoning


Zhuge Liang predicts the outcome



Hear the commentator


Cao Cao escapes

Is the cliffhanger a Chinese Invention ??


peter van emde boas: reconstructing games from stories lorentz center, leiden, 20150626...

Documents

reconstructing games

peter van emde boas

stories lorentz center

stories stratagem

budapest slide

tzu art of war

armed struggle slide

ancient china