gametheory
Game Theory
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Introduction
Game theory is an exciting field of mathematics with many applications in all spheres of sciences. It is responsible for many economists for getting Nobel price. Although it has spurned up larger interests in people, often they find it hard to understand once the initial interest dries up. Please read, the following page, as it relates game theory to popular cinema. The page contains detailed material I collected for a seminar, which I gave on final semester of my PG.
The Good, the Bad and the Ugly
I think that the final scene in this Clint Eastwood movie is the most outstanding example of game theory. Three men in a triangle -- each with a gun, a rock at the center of the three. It is up to each man to evaluate his situation. All are excellent shots. Who do they shoot?
Clint has supposedly put a message on a rock that holds the key to everything, but do the other two trust Clint to have actually written the correct answer? As the other two evaluate the situation, they realize they can't trust Clint to have written the answer on the rock -- therefore they can't shoot Clint who likely still has the answer. That means the other two can only shoot each other, but only one will likely hit before the other.
What they don't know is that Clint has given one an unloaded gun... Clint can ignore this one. The one Clint has to worry about with the loaded gun will try to kill the one with the unloaded gun. Neither will fire at Clint. Clint will fire at the one with the loaded gun. As the camera passes from one face to the other the audience is meant to figure out what each would do.
The guy with the loaded gun shoots at the guy with the unloaded gun -- Clint shoots the guy with the loaded gun. Game over. As with the hangings in the movie, he has dangled Duco out as bait while Clint takes the money.
The game is decided before it starts.
Clint sets up a situation where each evaluates their possible moves, but in reality, Clint has already won the game. Its a brilliant example of people making the best decisions based on the information available to them...and somebody manipulating the information available to them.
Game Theory links
http://en.wikipedia.org/wiki/Game_theory