DOC PREVIEW
UA EC 110 - Nash Equilibrium and Game Theory
Type Lecture Note
Pages 3

This preview shows page 1 out of 3 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

ECON 110 1st EditionLecture 25Outline of Last Lecture I. Comparison of Monopolies, Monopolistically Competitive Markets, and Perfectly Competitive MarketsII. Oligopoliesa. In Essenceb. Cartelsi. Definitionii. Problems that ariseOutline of Current Lecture I. Nash Equilibrium DefinitionII. Game theory DefinitionIII. Examplesa. The Prisoners’ Dilemmab. The Pricing Gamec. Pigs in a BoxCurrent Lecture – Nash Equilibrium and Game TheoryIn 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’ DilemmaLet’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. Now let’s analyze the best individual responses:- For Alo If Bill confesses, Al should confess, because 5 < 20.o If Bill does not confess, Al should confess, because 0 < 1. - For Billo 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!Now we again, list the outcomes for each player:- For Pepsi:o If Coke prices low, Pepsi will price low, because 5 > 2.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.KeyBlue = Bill’s strategies and outcomesRed = Al’s strategies and outcomes#s = time servedKEYRed = Coke’s strategies and profit outcomesBlue = Pepsi’s strategies and profit outcomes#s = Possible Profit (in 1000s of $)Confess Not ConfessConfess 5 , 5 0 , 20Not Confess 20 , 0 1 , 1Low HighLow 5 , 6 15 , 3 High 2 , 18 10 , 12We 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 StrategiesWeak Pig’s Strategies Push Wait Push -10 , 90 -10 , 100Wait 75 , 15 0 , 0 Let’s examine the options:- For the Weak pigo 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


View Full Document

UA EC 110 - Nash Equilibrium and Game Theory

Type: Lecture Note
Pages: 3
Download Nash Equilibrium and Game Theory
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Nash Equilibrium and Game Theory and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Nash Equilibrium and Game Theory 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?