This is a short clip about what rationality is usually taken to mean in models of rational action and what game theory brings to this important concept of rationality the social sciences. Generally the rational agent model for deicison making uses 3 key ideas to delineate the notion of rationality : (1) objectives and goals, (2) resources and feasibility constraints, and (3) contingencies and risks. Each of these ideas contributes to the key idea of constrained optimal choice in decision theory. But Game Theory adds a new dimension ….an awareness of the mutual awareness that all players are rational, with each being well aware that the other players know they are rational, and that they know they know…… This mutual awareness of rationality introduces some very distinctive ideas – and puzzles – about rational play in strategic situations that aren’t present in single person models of rational decision making where the “environment” for a decision, however complex, is explicitly viewed as either non-intelligent or blissfully ignorant of the roles of mutual conscious awareness of rationality.
This video clip defines the first discussion forum question , about how your ideas about what game theory is all about have changed after the first introductory lecture (this particular clip contains brief in-class discussions with 3 students from a couple of years ago then works through the key ideas in some textbook definitions of game theory).
Interesting complementary material to this introduction can be found here:
- the BBC Radio 4 “in our Time” podcast on game theory by Melvyn Bragg
- The introduction by the authors (an economist and 2 computer scientists) of the Coursera game theory course Game Theory Online is worth listening to as well (Indeed if you wish to learn a LOT more about game theory than you will in our introductory course – and are willing to learn/work with mathematics as a language for game theory – subscribe to this Youtube channnel AND take their coursera courses on game theory at coursera.org).
The next clip to watch is how to appreciate the difference between single-person agent and multi-person ideas about rationality.
This is a short clip about how to interpret the meaning of “rationality” in decision theory…augmented by an important new idea that game theory brings to this key concept in the social sciences.
The idea of mutual awareness of intelligence and rationality (and mutual awareness of mutual awareness of intelligence and rationality…and so on) is most easily appreciated – and remembered – by watching the “Battle of the Wits” from the Princess Bride. (book, film) . I own a dvd of the film, and I own the book, but becasue of ambiguity in copyright laws (and great risks to me and my ISPs if I get it wrong) I can’t risk enclosing the short clip “The Battle of Wits” from that movie. However, if you google “Battle of wits princess bride” you will find many many places on the web where you can watch that clip. Better yet – buy or rent the film used or new – it is a classic well worth owning. Here is a link to one Youtube page that has the film clip. And, if you want to read the portion of the book have a look at this Post ……or read and listen at the same time?? For educational purposes it “should be” OK to extract and use the small portion from the film without permission (but with acknowledgement)…that’s just “fair use” even in this age of the intellectual monopolists who have captured our political systems (see Boldrin and Levine’s “Against Intellectual Monopoly” here is the book in pdf form (yes the pdf is “free”) and lots of other cool stuff on Prof Levine’s home page) . Very different from the storytellers and theatrical companies of old who freely imitated one another and improvised/changed old stories – putting them in new wineskins and letting the highly competitive “performance marketplace” decide “who is right, and who is “dead” as Wesley would say. But ambiguity about what constitutes “fair use” and an anticipated lack of support from any University in NZ to challenge the intellectual monopoly system, deters me from putting up a segment of the Battle of Wits from the dvd that I actually own! The next clip to watch in this series for module 1 illustrates some interesting examples of reasoning about a simple game called “stop Go”, based on classroom interaction, student reasoning about their choices and perceptions in the game, interspersed with my commentary. It is a good way to gain experience with the reasoning processes used by relatively inexperienced but intelligent players trying to understand…and play…for money and for chocolate bars as prizes. Here at UC I do this “live” in class – over the internet and listening in it can be a bit boring – but we will have a recorded hangout (soon) on how to draw the game tree for and analyze this game
I own a dvd of the film (see wikipedia for more info) and I own the book (see wikipedia for more info ), but because of ambiguity in our current copyright laws (and great risks to me and my ISPs if I get it wrong) I can’t risk “sharing” with you short clip “The Battle of Wits” from that movie. However, if you google “Battle of wits princess bride” you will find many many places on the web where you can watch that clip. Here is a link to one Youtube page that has the film clip. And, if you want to read the portion of the book , or read and listen at the same time, see below . Better yet – buy or rent the film used or new – it is a classic well worth owning – search on “The Princess Bride” at Alice’s.
rave and rant : For educational purposes it “should be” OK to extract and use the small portion from the film without permission (but with acknowledgement)…that’s just “fair use” even in this age of the intellectual monopolists who have captured our political systems (see Boldrin and Levine’s “Against Intellectual Monopoly” here is the book in pdf form (yes the pdf is “free”) and lots of other cool stuff on Prof Levine’s home page) . Very different from the storytellers and theatrical companies of old who freely imitated one another and improvised/changed old stories – putting them in new wineskins and letting the highly competitive “performance marketplace” decide “who is right, and who is “dead” as Wesley would say.
The next clip to watch in this series for module 1 illustrates some interesting examples of reasoning about a simple game called “stop Go”, based on classroom interaction and student reasoning about their choices and perceptions in the game, interspersed with my commentary. It is a good way to gain experience with the reasoning processes used by relatively inexperienced but intelligent players trying to understand…and play…for money and for chocolate bars as prizes. Here at UC I do this game “live” in class – but over the internet and listening in it can be a bit boring – but we will have a recorded hangout (soon) on how to draw the game tree for and analyze this game.
The Battle of Wits: An excerpt from The Princess Bride, by William Goldman.
I have a Kindle edition of this book (I also own a copy of the DVD). Mass market paperback editions can be found everywhere on the web eg Amazon for about $2 used and $8 new. Page reference? Well ….on my kindle thats hard to describe. But its about a quarter of the way through!
Check out Wikipedia for more details on The Princess Bride
What about the video clip? You’ve already read my rant against the intellectual monopolists in 1.2 , so I won’t repeat that here. However, I can make available a small portion of the text of this scene w/o permission:
“The Battle of the wits” from The Princess Bride
I have made Vizzin the red player, Wesley, the man in black, the blue player….for future reference when we analyze this game….but also to make the text a little easier to read.
VIZZINI WAS WAITING for him.
Indeed, he had set out a little picnic spread. From the knapsack that he always carried, he had taken a small handkerchief and on it he had placed two wine goblets. In the center was a small leather wine holder and, beside it, some cheese and some apples. The spot could not have been lovelier: a high point of the mountain path with a splendid view all the way back to Florin Channel. Buttercup lay helpless beside the picnic, gagged and tied and blindfolded. Vizzini held his long knife against her white throat.
“Welcome,” Vizzini called when the man in black was almost upon them.
The man in black stopped and surveyed the situation.
“You’ve beaten my Turk,” Vizzini said. “It would seem so.”
“And now it is down to you. And it is down to me.”
“So that would seem too,” the man in black said, edging just a half-step closer to the hunchback’s long knife.
With a smile the hunchback pushed the knife harder against Buttercup’s throat. It was about to bring blood. “If you wish her dead, by all means keep moving,” Vizzini said.
The man in black froze. “Better,” Vizzini nodded.
No sound now beneath the moonlight.
“I understand completely what you are trying to do,” the Sicilian said finally, “and I want it quite clear that I resent your behavior. You are trying to kidnap what I have rightfully stolen, and I think it quite ungentlemanly.”
“Let me explain—” the man in black began, starting to edge forward.
“You’re killing her!” the Sicilian screamed, shoving harder with the
knife. A drop of blood appeared now at Buttercup’s throat, red against white.
The man in black retreated. “Let me explain,” he said again, but from a distance.
Again the hunchback interrupted. “There is nothing you can tell me I do not already know. I have not had the schooling equal to some, but for knowledge outside of books, there is no one in the world close to me. People say I read minds, but that is not, in all honesty, true. I merely predict the truth using logic and wisdom, and I say you are a kidnapper, admit it.”
“I will admit that, as a ransom item, she has value; nothing more.”
“I have been instructed to do certain things to her. It is very important that I follow my instructions. If I do this properly, I will be in demand for life. And my instructions do not include ransom, they include death. So your explanations are meaningless; we cannot do business together. You wish to keep her alive for ransom, whereas it is terribly important to me that she stop breathing in the very near future.”
“Has it occurred to you that I have gone to great effort and expense, as well as personal sacrifice, to reach this point,” the man in black replied.
“And that if I fail now, I might get very angry. And if she stops breathing in the very near future, it is entirely possible that you will catch the same fatal illness?”
“I have no doubt you could kill me. Any man who can get by Inigo and Fezzik would have no trouble disposing of me. However, has it occurred to you that if you did that, then neither of us would get what we want—you having lost your ransom item, me my life.”
“We are at an impasse then,” said the man in black.
“I fear so,” said the Sicilian. “I cannot compete with you physically, and you are no match for my brains.”
“You are that smart?”
“There are no words to contain all my wisdom. I am so cunning, crafty and clever, so filled with deceit, guile and chicanery, such a knave, so shrewd, cagey as well as calculating, as diabolical as I am vulpine, as tricky as I am untrustworthy … well, I told you there were not words invented yet to explain how great my brain is, but let me put it this way: the world is several million years old and several billion people have at one time or another trod upon it, but I, Vizzini the Sicilian, am, speaking with pure candor and modesty, the slickest, sleekest, sliest and wiliest fellow who has yet come down the pike.”
“In that case,” said the man in black, “I challenge you to a battle of wits.”
Vizzini had to smile. “For the Princess?”
“You read my mind.”
“It just seems that way, I told you. It’s merely logic and wisdom. To the death?”
“I accept,” cried Vizzini. “Begin the battle!”
“Pour the wine,” said the man in black.
Vizzini filled the two goblets with deep-red liquid.
The man in black pulled from his dark clothing a small packet and handed it to the hunchback. “Open it and inhale, but be careful not to touch.”
Vizzini took the packet and followed instructions. “I smell nothing.”
The man in black took the packet again. “What you do not smell is called iocane powder. It is odorless, tasteless and dissolves immediately in any
kind of liquid. It also happens to be the deadliest poison known to man.”
Vizzini was beginning to get excited.
“I don’t suppose you’d hand me the goblets,” said the man in black. Vizzini shook his head. “Take them yourself. My long knife does not
leave her throat.”
The man in black reached down for the goblets. He took them and turned away.
Vizzini cackled aloud in anticipation.
The man in black busied himself a long moment. Then he turned again with a goblet in each hand. Very carefully, he put the goblet in his right hand in front of Vizzini and put the goblet in his left hand across the kerchief from the hunchback. He sat down in front of the left-hand goblet, and dropped the empty iocane packet by the cheese.
“Your guess,” he said. “Where is the poison?”
“Guess?” Vizzini cried. “I don’t guess. I think. I ponder. I deduce. Then I decide. But I never guess.”
“The battle of wits has begun,” said the man in black. “It ends when you decide and we drink the wine and find out who is right and who is dead. We both drink, need I add, and swallow, naturally, at precisely the same time.”
“It’s all so simple,” said the hunchback. “All I have to do is deduce, from what I know of you, the way your mind works. Are you the kind of man who would put the poison into his own glass, or into the glass of his enemy?”
“You’re stalling,” said the man in black.
“I’m relishing is what I’m doing,” answered the Sicilian. “No one has challenged my mind in years and I love it. … By the way, may I smell both goblets?”
“Be my guest. Just be sure you put them down the same way you found them.”
The Sicilian sniffed his own glass; then he reached across the kerchief for the goblet of the man in black and sniffed that. “As you said, odorless.”
“As I also said, you’re stalling.”
The Sicilian smiled and stared at the wine goblets. “Now a great fool,” he began, “would place the poison in his own goblet, because he would know
that only another great fool would reach first for what he was given. I am clearly not a great fool, so I will clearly not reach for your wine.”
“That’s your final choice?”
“No. Because you knew I was not a great fool, so you would know that I would never fall for such a trick. You would count on it. So I will clearly not reach for mine either.”
“Keep going,” said the man in black.
“I intend to.”
The Sicilian reflected a moment. “We have now decided the poisoned cup is most likely in front of you. But the poison is powder made from iocane and iocane comes only from Australia and Australia, as everyone knows, is peopled with criminals and criminals are used to having people not trust them, as I don’t trust you, which means I can clearly not choose the wine in front of you.”
The man in black was starting to get nervous.
“But, again, you must have suspected I knew the origins of iocane, so you would have known I knew about the criminals and criminal behavior, and therefore I can clearly not choose the wine in front of me.”
“Truly you have a dizzying intellect,” whispered the man in black.
“You have beaten my Turk, which means you are exceptionally strong,
and exceptionally strong men are convinced that they are too powerful ever to die, too powerful even for iocane poison, so you could have put it in your cup, trusting on your strength to save you; thus I can clearly not choose the wine in front of you.”
The man in black was very nervous now.
“But you also bested my Spaniard, which means you must have studied, because he studied many years for his excellence, and if you can study, you are clearly more than simply strong; you are aware of how mortal we all are, and you do not wish to die, so you would have kept the poison as far from yourself as possible; therefore I can clearly not choose the wine in front of me.”
“You’re just trying to make me give something away with all this chatter,” said the man in black angrily. “Well it won’t work. You’ll learn nothing from me, that I promise you.”
“I have already learned everything from you,” said the Sicilian. “I know
where the poison is.”
“Only a genius could have deduced as much.”
“How fortunate for me that I happen to be one,” said the hunchback, growing more and more amused now.
“You cannot frighten me,” said the man in black, but there was fear all through his voice.
“Shall we drink then?”
“Pick, choose, quit dragging it out, you don’t know, you couldn’t know.” The Sicilian only smiled at the outburst. Then a strange look crossed his features and he pointed off behind the man in black. “What in the world can that be?” he asked.
The man in black turned around and looked. “I don’t see anything.” “Oh, well, I could have sworn I saw something, no matter.” The Sicilian
began to laugh.
“I don’t understand what’s so funny,” said the man in black.
“Tell you in a minute,” said the hunchback. “But first let’s drink.” And he picked up his own wine goblet.
The man in black picked up the one in front of him. They drank.
“You guessed wrong,” said the man in black.
“You only think I guessed wrong,” said the Sicilian, his laughter ringing louder. “That’s what’s so funny. I switched glasses when your back was turned.”
There was nothing for the man in black to say.
“Fool!” cried the hunchback. “You fell victim to one of the classic blunders. The most famous is ‘Never get involved in a land war in Asia,’ but only slightly less well known is this: ‘Never go in against a Sicilian when death is on the line.'”
He was quite cheery until the iocane powder took effect.
The man in black stepped quickly over the corpse, then roughly ripped the blindfold from the Princess’s eyes.
“I heard everything that happ—” Buttercup began, and then she said “Oh” because she had never been next to a dead man before. “You killed
him,” she whispered finally.
“I let him die laughing,” said the man in black. “Pray I do as much for you.” He lifted her, slashed her bonds away, put her on her feet, started to pull her along.
“Please,” Buttercup said. “Give me a moment to gather myself.” The man in black released his grip.
Buttercup rubbed her wrists, stopped, massaged her ankles. She took a final look at the Sicilian. “To think,” she murmured, “all that time it was your cup that was poisoned.”
“They were both poisoned,” said the man in black. “I’ve spent the past two years building up immunity to iocane powder.”
Buttercup looked up at him. He was terrifying to her, masked and hooded and dangerous; his voice was strained, rough. “Who are you?” she asked.
“I am no one to be trifled with,” replied the man in black. “That is all you ever need to know.” And with that he yanked her upright. “You’ve had your moment.” Again he pulled her after him, and this time she could do nothing but follow.
They moved along the mountain path. The moonlight was very bright, and there were rocks everywhere, and to Buttercup it all looked dead and yellow, like the moon. She had just spent several hours with three men who were openly planning to kill her. So why, she wondered, was she more frightened now than then? Who was the horrid hooded figure to strike fear in her so? What could be worse than dying? “I will pay you a great deal of money to release me,” she managed to say.
The man in black glanced at her. “You are rich, then?”
“I will be,” Buttercup said. “Whatever you want for ransom, I promise I’ll get it for you if you’ll let me go.”
The man in black just laughed. “I was not speaking in jest.”
“You promise? You? I should release you on your promise? What is that worth? The vow of a woman? Oh, that is very funny, Highness. Spoken in jest or not.”
They proceeded along the mountain path to an open space. The man in black stopped then. There were a million stars fighting for prominence and for a moment he seemed to be intent on nothing less than……
This is one of the better classroom game experiences for the Stop Go game . I’ve edited out a lot of the slow detail (eg selecting and recording student players, “banter” type stories, etc) and kept some VERY interesting classroom, student reasoning and questioning about this game…. but we still end up with 22 minutes!! The live “commentary” here is about how one develops an understanding of this game through learning and experience and the sort of assumptions that have to be made/are made in order to get the theory “working” to make some predictions. Enjoy.
Next , and last in Module 1, we begin to structure our thinking about games using first (and most simply) the PDIP concept, then second, the 6 questions to ask about any type of strategic interaction (game). After that we turn to Module 2 – Sequential Games of Complete and Perfect Information.