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by: Allie West II


Allie West II

GPA 3.51


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Class Notes
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This 16 page Class Notes was uploaded by Allie West II on Thursday October 29, 2015. The Class Notes belongs to CSCI 5582 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/231991/csci-5582-university-of-colorado-at-boulder in ComputerScienence at University of Colorado at Boulder.

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Date Created: 10/29/15
Game Theory 1 ZeroSum Games and the Prisoner s Dilemma CSC15582 Fall 2007 Assignments 0 Reading for this week Axelrod at website 0 Problem Set 4 due Thursday Dec 6 0 Problem Set 2 back today Clyde Clam up Stool Pigeon Clam up 1 year 20 years 1 year 0 years Bonnie 0 years 10 years Stool Plgeon 20 years 10 years Prisoner s Dilemma The Formal Conditions DCgtCCgtDDgtCD CC gt DC CD2 Blue Cooperate Defect Cooperate 3 0 3 5 Red 5 1 Defect 0 1 Game Theory Basic Taxonomy Zero vs non zero sum Two vs N person games Finite vs infinite number of Choices Iterated vs non iterated games Games of perfect information Two Person Zero Sum Games The notion of a dominant choice Tricks for reducing game matrices The solution of a zero sum game The value of a game The minimaX theorem Pure vs Mixed strategies Symmetric games Blue A A 5 Red B 4 Red Blue 10 11 Blue Worst I can do 4 5 9 3 Red 8 4 3 7 7 6 8 9 7 2 4 6 Worst I can do Scissors Paper Stone Scissors 0 1 1 1 Paper 1 0 1 1 0 Stone Blue Red B 0 12 Determining a Mixed Strategy We are looking for a mixed strategy for Red With probability p for choice A and l p for choice B Suppose Blue plays only C the left column Then the value V of the game to Red is p 11p 0 p Suppose Blue plays only D the right column Then the value of the game to Red is p 0 l p 12 12 p2 The value of the game v to Red should be the same regardless of these choices for Blue So we have p 12 p2 or p 13 Expected score per round for Red Probability of Red playing A 1 The Minimax Theorem in Game Theory 0 Applies to zerosum twoperson finite games 0 The minimax theorem says that in such a game there is a value V for the game the same value V for both players Given an optimal strategy possibly a mixed strategy each player can be assured on average of obtaining at least V for the game regardless of What the other player does 0 What this means essentially is that both players can examine such a matrix and determine beforehand and regardless of the other player s plan What they need to do to ensure receiving an average of V for the game


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