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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Lecture number:
25
Pages:
3
Type:
Lecture Note
School:
University of Alabama
Course:
Ec 110 - Prin of Microeconomics
Edition:
1
Unformatted text preview:

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 Bill does not confess Al should confess because 0 1 For Bill o If Al confesses Bill should confess because 5 20 o If Al does not confess Bill should confess because 0 1 Nash Equilibrium Confess confess because at that place there is nothing either can do on their own to be better off The best option is both not confess but Bill cannot guarantee that Al will follow through and visa versa Ex 2 Next let s play the Pricing Game The players are Coke and Pepsi and their possible strategies are fixing a high price or fixing a low price Let s diagram it KEY Now Low High Low 5 6 15 3 High 2 18 10 12 Red Coke s strategies and profit outcomes we again listBlue the outcomes for each player Pepsi s strategies and profit outcomes For Pepsi o If Coke prices low Pepsi will price low because 5 2 s Possible Profit in 1000s of o If Coke prices high Pepsi will low because 15 10 o NOTE Pepsi in this case has a Dominant Strategy or pricing low meaning that no matter what that is what they will do For Coke o If Pepsi prices low Coke will also price low because 6 3 o If Pepsi prices high Coke will still price low because 18 12 o Coke also has a dominant strategy of pricing low The Nash Equilibrium will be at low low because without working together neither can do any better Ex 3 Last Example Pigs in a Box We have two pigs in a box a weak pig and a strong pig On one end of the box is a food dispenser On the opposite wall is a button which dispenses 100 calories worth of food every time it is pushed It takes ten calories to walk from the button to the dispenser The pigs both have two options push the button and then walk to the food dispenser or wait by the food dispenser If the weak pig were to push the button the strong pig would eat all the food before he could get there If the strong pig were to push the button the weak pig would have eaten 75 calories of food by the time he got there If they both push the button the strong pig would get there first and eat all the food Strong Pig s Strategies Weak Pig s Strategies Push Wait Push 10 90 10 100 Wait 75 15 0 0 Let s examine the options For the Weak pig o If the strong pig pushes the button the weak pig will wait 75 10 o If the strong pig waits the weak pig will wait 0 10 o The weak pig s dominant strategy is to wait For the Strong pig o If the weak pig pushes the button the strong pig will wait 100 90 o If the weak pig waits the strong pig will push the button 15 0 o The Strong pig does not have a dominant strategy


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