UA EC 110 - Nash Equilibrium and Game Theory (3 pages)

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Nash Equilibrium and Game Theory

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Nash Equilibrium and Game Theory


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University of Alabama
Ec 110 - Prin of Microeconomics

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ECON 110 1st Edition Lecture 25 Outline of Last Lecture I Comparison of Monopolies Monopolistically Competitive Markets and Perfectly Competitive Markets II Oligopolies a In Essence b Cartels i Definition ii Problems that arise Outline of Current Lecture I Nash Equilibrium Definition II Game theory Definition III Examples a The Prisoners Dilemma b The Pricing Game c Pigs in a Box Current Lecture Nash Equilibrium and Game Theory In order to look at game theory we first need to understand the Nash Equilibrium In essence this occurs when the individual players cannot do anything on their own to make themselves better off NOTE It is not the mutually best choice when they are working together but the best choice that each can make based off the other s decision when they are not working together Now Game Theory is a formal way of looking at strategic interactions It requires a set of players a set of strategies and a set of payoffs Ex 1 The Prisoners Dilemma Let s say we have to guys who were accused of a crime Al and Bill The police think they did it but they don t have any evidence to link them to the crime The police bring both in for separate questioning and are trying to get them to confess If one confesses and the other doesn t the one that confesses will get off and the other will get 20 years in prison If neither confesses they both get a year If they both confess they get five years Obviously the best These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute scenario for both is that neither confesses but neither has a guarantee that the other will follow through with the agreement We diagram the situation as follows Confess Not Confess Confess 5 5 0 20 Not Confess 20 0 1 1 Key Blue Bill s strategies and outcomes Now let sRed analyze the best individual responses Al s strategies and outcomes For Al s time served o If Bill confesses Al should confess because 5 20 o If

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