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Avinash Dixit writes in Restoring Fun to Game Theory[1]: Many movies contain scenes that illustrate some aspect of strategic interaction. These scenes can be screened in class as an introduction to that topic, and a discussion can lead to theorectical analysis of it.

Brinkmanship: Many movies have scenes that deal with the question of how to get some vital information that only your adversary possesses because he knows that the threat of killing him in not credible. The situation plays out differently in High Wind in Jamaica, Crimson Tide, The Maltese Falcon, and The Gods Must Be Crazy... In The Maltese Falcon, the hero, Samuel Spade (played by Humphrey Bogart), is the only person who knows where the priceless gem-studded falcon is hidden, and the chief villain, Caspar Gutman (Sydney Greenstreet), is threatening him for his information. This produces a classic exchange, here cited from the book (Hammet 1930, 223-24) but reproduced almost verbatim in the movie.
Spade flung his words out with a brutal sort of carelessness that gave them more weight than they could have got from dramatic emphasis or from loudness. "If you kill me, how are you going to get the bird? If I know you can't afford to kill me till you have it, how are you going to scare me into giving it to you?"

Gutman cocked his head to the left and considered these questions. His eyes twinkled between puckered lids. Presently, he gave his genial answer: "Well, sir, there are other means of persuasion besides killing and threatening to kill."

"Sure," Spade agreed, "but they're not much good unless the threat of death is behind them to hold the victim down. See what I mean? If you try something I don't like I won't stand for it. I'll make it a matter of your having to call it off or kill me, knowing you can't afford to kill me."

"I see what you mean." Gutman chuckled. "That is an attitude, sir, that calls for the most delicate judgement on both sides, because, as you know, sir, men are likely to forget in the heat of action where their best interests lie and let their emotions carry them away."

Spade too was all smiling blandness. "That's the trick, from my side," he said, "to make my play strong enough that it ties you up, but yet not make you mad enough to bump me off against your better judgment."
The class discussion can explore the nature of these strategies. The scene can be seen as an example of Schelling's (1960, 17-18, [The Strategy of Conflict]) idea of the (strategic) rationality of (seeming) irrationality; Gutman is making his threat credible by pointing out that he might be irrationally. It is better seen as an example of the dynamic game of brinkmanship (Schelling 1960, ch.8; 1966, ch. 3). Both parties, by persisting in their actions--Gutman in his torture and Spade in his defiance--are raising the risk that Gutman may get angry and do something against his own rational interest. Each is exploring the risk tolerance of the other, in the hope that it is lower than his own risk tolerance so that the other will blink first. A more formal analysis of this in the context of the Cuban missile crisis is found in Dixit and Skeath (2004, ch. 14,[Games of Strategy]).
The scene from The Gods Must Be Crazy makes this escalation of risk more explicit. An assassination attempt on the dictator of an African country has failed, and one of the team of gunmen has been captured. He is being interrogated for the location of the group's headquaters and the leader. The scene is in the inside of the helicopter. The blindfolded gunman is standing with his back to the open door. Above the noise of the rotors, the army officer questions the gunman a couple of times and gets only shakes of the head. Then he simply pushes the gunman out the door. The scene switches to the outside of the helicopter, which we now see is just barely hovering above the ground, and the gunman has fallen [2 meters] on his back. The army officer appears at the door and says, "The next time it will be a little higher."
Brinkmanship arises in many economic contexts, most notably that of wage bargaining where the risk of a strike or of a lockout increases as protracted negotiations fail to produce results. Understanding the subtleties and the risks of this strategy is therefore an important part of an exonomist's education, and these movie scenes illustrate it in memorable ways.

Nash Equilibrium: ... The crucial scene from the movie, where Nash is supposed to have discovered his concept of equilibrium, shows him in a bar with three male friends. A blonde and her four brunette friends walk in. All four men would like to win the blonde's favour. However, if they all approach her, each will stand at best a one-fourth chance; actually, the movie seems to suggest that she whould reject all four. The men will have to turn to the brunettes, but then the brunettes will reject them also, because "no one likes to be second choice." In the movie, Nash says that the solution is for them all to ignore the blonde and go for the brunettes. One of the other men thinks this is just a ploy on Nash's part to get the others to go for the brunettes so he can be the blonde's sole suitor. If one thinks about the situation using game theory, the Nash character is wrong and the friend is right. The strategy profile where all men go for the brunettes is not a Nash equilibrium: Given the strategies of the others, any one of them gains by deviating and going for the blonde. In fact, Anderson and Engers [pdf, opens with errors] (2002) show that the game has multiple equilibria, but the only outcome that cannot be a Nash equilibrium is the supposedly brilliant solution found by the Nash character.

Mixed Strategies: The concept of mixed strategies is often initially counterintuitive. Although many situations in sports serve to introduce it, I like one scene from The Princess Bride, a whimsical comedy that has the added advantage of being a favorite teen movie. In this scene, the hero (Westley) challenges one of the villains (Vizzini) to a duel of wits. Westley will poison one of two wine cups without Vizzini observing this action and set one in front of each of them. Vizzini will decide from which cup he will drink; Westley then must drink from the other cup. Vizzini goes through a whole sequence of arguments as to why Westley would or would not choose to poison one cup or the other. Finally, he believes he knows which cup is safe and drinks from it. Westley drinks form the other. Just as Vizzini is laughing and advising Westley to "never go against a Sicilian when death is on the line," Vizzini drops dead.
Pause the videotape or disc at this point and have a brief discussion. The students will quickly see that each of Vizzini's arguments is inherently self-contradictory. If Westley thinks through to the same point that leads Vizzini to believe that a particular cup will contain the poison, he should instead put the poison in the other cup. Any systematic action can be thought through and defeated by the other player. Therefore, the only correct strategy is to be unsystematic or random.

Asymmetric Information: Actually, this is not the main point of the story. Resume the tape or disc. The princess is surprised to find that Westley had put the poison in the cup he placed closer to himself. "They were both poisoned," he replies. "I have been building up immunity to Iocaine for years." Thus the game being played was really one of asymmetric information; Vizzini did not know Westley's payoffs and did not think the strategy of poisoning both cups was open to him. At this point, you can show a clip from another movie classic, Guys and Dolls. Sky Masterson recalls advice from his father: "Son, no matter how far you travel, or how smart you get, always remember this: Some day, somewhere, a guy is going to come to you and show you a nice brand-new deck of cards on which the seal is never broken, and this guy is going to offer to bet you that the jack of spades will jump out of this deck and squirt cider in your ear. But son, do not bet him, for as sure as you do you are going to get an ear full of cider" (Runyon 1933 [1992]).

Dr. Strangelove. ... A good case can be made for screening the whole movie and discussing it.

[1] Journal of Economic Education, Summer 2005, Volume 36, Number 3
Johan Richter (guest) meinte am 24. Nov, 22:43:
About the Nash movie. I thought "Nash"s point was that the equilibrium where everbody follows his one self-interest leads to a worse overall outcome.
This is strengthend by the fact that the movie later talks about Nash challenging the dominant opion in economics that if you follow your own interest you benefit the common interest. 
Mahalanobis antwortete am 25. Nov, 01:41:
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This is strengthend by the fact that the movie later talks about Nash challenging the dominant opion in economics that if you follow your own interest you benefit the common interest.
I must have been sleeping during that part. But think of the price-setting of oligopolies. Companies play the Prisoner's dilemma, therefore they sell at marginal cost (Bertrand model) and by doing so they benefit the public interest => If you follow your own interest you benefit the common interest. QED. ;-DD 
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radek (guest) meinte am 26. Nov, 00:50:
"Nash Equilibrium..."

I thought the movie was simply confusing the idea of Nash Equilibrium with the Nash Bargaining Solution and winding up with something that was neither (not just in that place). 
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Remember the Nash bargaining solution defines axioms (four, namely Pareto-efficiency, utility independence of affine transformations, independence of irrelevant alternatives, and symmetry) which a point (set) in the set of feasible allocations should fulfill.
Concerning the Nash equilibrium of the "bar-approaching blond girl game", it's very difficult to give the Nash equilibria. I think the information structure, the utilities and so on can be constructed such that almost any possible strategy combination could be a (bayesian) Nash equilibrium. 
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