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

1. Peter van Emde Boas, ILLC-FNWI-UvA and Bronstee.com Software & Services B.V. Workshop Clusters, Games and Axioms (previously presented at CiE 2014 – Budapest) Reconstructing games from storieswhy we should want to do it and why it will be hard to do so 20150626

2. 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

3. 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

4. Sources used

5. Sources • Sun Tzu The Art of War around 500 BC • Romance of the Three Kingdoms around 1400 AD • describing events during the period 168 – 260 AD (A period of • Civil war leading to the end of the Han Dynasty) • The 13 chapters in the classic Sun Tzu Art of War • Strategic Assessments 8 Adaptations • Doing Battle 9 Maneuvring Armies • Planning a Siege 10 Terrain • Formation 11 Nine Grounds • Force 12 Fire Attack • Emptiness and Fullness 13 On the use of Spies • Armed Struggle

6. Motivating Quote 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. Did the ancient Chinese actually use such an Analysis? What could the Chinese have analyzed in a concrete situation?

7. 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?

8. 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, …?

9. 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!

10. 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

11. 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

12. 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

13. 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?

14. 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.

15. 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

16. 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

17. Example: the ambush at Huarong Yanjing Wang, ph.d. thesis ILLC, 20100921, Epistemic Modelling & Protocol Dynamics, ch 1

18. 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

19. V M V -1/1 1/-1 M 1/-1 -1/1 The formal representation Cao Cao does not want to be ambushed He can take the Valley or the Mountain road Lord 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

20. 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

21. What Sun Tzu teaches The concept of Deception involved is mentioned in Sun Tzu. But no higher order Theory-of-mind reasoning. The story actually involves third Order Theory-of-mind Reasoning; Sun Tzu, the Art of War, ch 1; ed. Wu Rusong

22. 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

23. 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

24. 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.

25. 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

26. The end

27. Some Sun Tzu quotes Wu Rusong ch8 Clarey ch3

28. Cao Cao’s reasonings Romance of the three Kingdoms, ch 50

29. Zhuge Liang’s resoning Romance of the three Kingdoms, ch 49

30. Romance of the three Kingdoms, ch 49 Zhuge Liang predicts the outcome

31. Hear the commentator

32. Cao Cao escapes Romance of the three Kingdoms, ch 50 Is the cliffhanger a Chinese Invention ??