lecture6 - Lecture 6 Game Theory Key Terms in Lecture Game...

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Lecture 6: Game Theory
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•G a m e –p layers – actions – strategies – payoffs • Extensive Form • Normal Form • Nash Equilibrium • Dominant Strategy Key Terms in Lecture
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Game Theory… • In economics we consider an agent choosing actions to maximize its objective function (subject to constraints) – e.g.: choose how much to consume subject to budget constraint • Up to now, we have postulated that each given action is associated with an outcome (possibly probabilistically) – We have not worried about interactions between different agents • i.e., the actions of one agent have not affected the decision of another • What if the impact of Bob’s action on Bob’s utility function depends on what action Joe takes? And what if the impact of Joe’s action on Joe’s utility function depends on what action Bob takes? • Then when Bob chooses his action he has to worry about what Joe does, and vice versa.
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Game Theory example • In the movie “A Beautiful Mind” John Nash and 3 male friends are in a bar… and in walk 5 women • All the men agree that one of the women is the “best,” whatever that means – That is, each would most like to marry the best • Each guy can talk to at most one girl • They think that if only one guy talks to a girl, he marries her •I f x of the guys talk to one of the girls, they each have a 1/x chance of marrying her. • What should they do?
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Game Theory example • If this were a problem like what we’ve been working on: – We’d focus on one guy and say: • He chooses with whom to speak in order to maximize his utility subject to a budget constraint – But this doesn’t work now b/c the impact of any action of his on his own utility depends on the actions of the other guys (and vice versa) • We have to figure out other people’s strategies before we know the impact of each action on his utility
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Game Theory example • In the movie, Nash says that they normally all converge on the “best,” and none get married • Nash tells all the guys to talk to one of the 4 girls who’s not the best • This way each manages to get married – We’ll discuss whether this is even a Nash Equilibrium… • This is obviously a silly example
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lecture6 - Lecture 6 Game Theory Key Terms in Lecture Game...

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