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## MATH GAME THEORY

by: Kaylin Wehner

121

0

2

# MATH GAME THEORY MATH 0167

Kaylin Wehner
UCLA
GPA 3.55

Staff

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COURSE
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KARMA
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## Popular in Mathematics (M)

This 2 page Study Guide was uploaded by Kaylin Wehner on Friday September 4, 2015. The Study Guide belongs to MATH 0167 at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 121 views. For similar materials see /class/177829/math-0167-university-of-california-los-angeles in Mathematics (M) at University of California - Los Angeles.

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Date Created: 09/04/15
Math 167 Midterm Study Guide Updated 2607 Written by Akemi Kashiwada Midterm February 9 2007 Disclaimer This is just a guide to help you study for the midtermi The material in this study guide will not necessarily be on the midterm and vice versa This is just what I would knowstudy ifl were a student in Math 167 There may be some typosmistakes so do not just use this to study ie be sure to look at old homeworks notes book etc Some of the exercises have been taken from the text Feel free to ask me questions during of ce hours discussion or via email akashiwadaQucla edu if anything here is unclear 1 Topics to Know The following is a list of topics that I feel are the most important that welve covered so far As I havenlt seen your midterm it is possible that are will be other topics covered on your exam that are not listed 0 Extensive form of game 7 Given a story be able to construct the corresponding game tree 7 Know how to solve a game in extensive form ie Zermelo s algorithmi Zermelo s algorithm gives you subgameperfect equilibria which are the subset of Nash equilibria that are Nash in every subgamei If the game is not strictly competitive then you need to do a separate analysis for each indifferent choice at any no er 0 Strategic form of game 7 Know how to construct strategic form from extensive formi 7 Solving games in strategic form involves nding the Nash equilibria or saddle pointsi Methods to nd Nash equilibria include 96 Movement diagram Minimaxmaximin o How to nd value of game 0 Strategy stealing argument 0 How to calculate probabilities independent conditional and expected value 0 Lotteries 7 Know how to construct lotteries from story 7 Converting compound lotteries to simple lotteries Math 167 2 2 Exercises Here are some example problems that 1 hope Will help you prepare for the midterm The last three are from last quarter7s midterm 1 also suggest looking oVer the questions in the book similar to the ones you Were assigned The exercises labelled With 5 are from Straf n 1 3 Find the saddle points of the following strictly competitive game H 3 For the games in Figure 1 a Find the subgameperfect equilibria b Write the game in strategic form c Find the Nash equilibria of this game Are there more than subgameperfect equilibria at b Figure 1 Games to be analyzed in Exercies 7 4 Exercises 224 and 225 in Binmore 5 In a Version of the game pickiupibricks tWo players alternate taking 1 or 2 bricks from a pile that starts With n bricks The players are called 1 and 117 With 1 being the one Who moVes rst The Winner is the player Who remoVes the last brick Draw the game tree and compute the Value of this game When n 4

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