Game Theory Solutions 1 Find the saddle point for the game having the following payoff table. Use the minimax criterion to find the best strategy for.

Slides:



Advertisements
Similar presentations
Introduction to Game Theory
Advertisements

GAME THEORY.
Two Player Zero-Sum Games
Module 4 Game Theory To accompany Quantitative Analysis for Management, Tenth Edition, by Render, Stair, and Hanna Power Point slides created by Jeff Heyl.
Name: Trương Hoài Anh Facebook: Quasar Hoaianh
Two-Person, Zero-Sum Game: Advertising TV N TVN 0 TV N TVN Column Player: Row Player: Matrix of Payoffs to Row.
Game Theory Assignment For all of these games, P1 chooses between the columns, and P2 chooses between the rows.
Game Theory S-1.
15 THEORY OF GAMES CHAPTER.
APPENDIX An Alternative View of the Payoff Matrix n Assume total maximum profits of all oligopolists is constant at 200 units. n Alternative policies.
Two-Player Zero-Sum Games
1 Chapter 4: Minimax Equilibrium in Zero Sum Game SCIT1003 Chapter 4: Minimax Equilibrium in Zero Sum Game Prof. Tsang.
© 2015 McGraw-Hill Education. All rights reserved. Chapter 15 Game Theory.
Peter Lam Discrete Math CS. Outline  Use game theory to solve strictly determining games  Non strictly games  Create models for games  Find optimal.
9.2 Mixed Strategies Two players, Robert and Carol, play a game with payoff matrix (to Robert): Is the game strictly determined? Why? Robert has strategy:
Part 3: The Minimax Theorem
Game Theory Part 5: Nash’s Theorem.
Non-cooperative Game Theory Notes by Alberto Bressan.
Homework Solutions MGMT E-5070 Game Theory Computer-Based Manual.
Game Theory and Applications following H. Varian Chapters 28 & 29.
Lectures in Microeconomics-Charles W. Upton Minimax Strategies.
Game Theory Objectives:
To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna S-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Supplement 1.
Game Theory.
Minimax Strategies. Everyone who has studied a game like poker knows the importance of mixing strategies. –With a bad hand, you often fold –But you must.
Game Theory. Your Task  Split into pairs and label one person A and the other B.  You are theoretically about to play a game involving money. Player.
Game Theory.
To accompany Quantitative Analysis for Management,9e by Render/Stair/Hanna M4-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Module 4 Game.
Game Theory Warin Chotekorakul MD 1/2004. Introduction A game is a contest involving to or more players, each of whom wants to win. Game theory is the.
Q 5-2 a. E = Efficiency score wi = Weight applied to i ’s input and output resources by the composite hospital.
Chapter 14 Game Theory to accompany Operations Research: Applications and Algorithms 4th edition by Wayne L. Winston Copyright (c) 2004 Brooks/Cole, a.
1 CRP 834: Decision Analysis Week Four Notes. 2 Review Game Theory –Classification and Description –Two Person Zero-Sum Game Game w/ Dominating Strategy.
A Little Game Theory1 A LITTLE GAME THEORY Mike Bailey MSIM 852.
Chapter 11 Game Theory Math Game Theory What is it? – a way to model conflict and competition – one or more "players" make simultaneous decisions.
\ B A \ Draw a graph to show the expected pay-off for A. What is the value of the game. How often should A choose strategy 1? If A adopts a mixed.
Game Theory Presented By: - Mrityunjay Sanwalot SMU II Sem.
Game Theory, Part 2 Consider again the game that Sol and Tina were playing, but with a different payoff matrix: H T Tina H T Sol.
1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edward’s University.
1 CRP 834: Decision Analysis Week Three Notes. 2 Review Decision-Flow Diagram –A road map of all possible strategies and outcomes –At a decision fork,
When dealing with a model, we use the letter  for the mean. We write or, more often, replacing p by, Instead of , we can also write E(X ). ( Think of.
Part 3 Linear Programming
Game Theory Optimal Strategies Formulated in Conflict MGMT E-5070.
Lecture 12. Game theory So far we discussed: roulette and blackjack Roulette: – Outcomes completely independent and random – Very little strategy (even.
A Closer Look at Game Theory: The Hat Puzzle By Julia Greenberger.
1. 2 Some details on the Simplex Method approach 2x2 games 2xn and mx2 games Recall: First try pure strategies. If there are no saddle points use mixed.
1 a1a1 A1A1 a2a2 a3a3 A2A Mixed Strategies When there is no saddle point: We’ll think of playing the game repeatedly. We continue to assume that.
Tables Learning Support
GAME THEORY Day 5. Minimax and Maximin Step 1. Write down the minimum entry in each row. Which one is the largest? Maximin Step 2. Write down the maximum.
9.2 Mixed Strategy Games In this section, we look at non-strictly determined games. For these type of games the payoff matrix has no saddle points.
Day 9 GAME THEORY. 3 Solution Methods for Non-Zero Sum Games Dominant Strategy Iterated Dominant Strategy Nash Equilibrium NON- ZERO SUM GAMES HOW TO.
DECISION MODELS. Decision models The types of decision models: – Decision making under certainty The future state of nature is assumed known. – Decision.
Problems Decision Making under Uncertainty Rahul Chandra.
Game Theory [geym theer-ee] : a mathematical theory that deals with the general features of competitive situations in a formal abstract way.
Chapter 5 Supplement Decision Theory.
Planning of Barus & Holley Addition
Solve the following game graphically
Chapter 6 Game Theory (Module 4) 1.
Game Theory.
نظام التعليم المطور للانتساب
Solutions Sample Games 1
Game Theory Solutions 1 Find the saddle point for the game having the following payoff table. Use the minimax criterion to find the best strategy for.
نظام التعليم المطور للانتساب
Game Theory II Solutions 1
Game Theory II Solutions 1
Game Theory Day 3.
9.3 Linear programming and 2 x 2 games : A geometric approach
Operations Research: Applications and Algorithms
MinMax Theorem John von Neumann
Operations Research: Applications and Algorithms
Presentation transcript:

Game Theory Solutions 1 Find the saddle point for the game having the following payoff table. Use the minimax criterion to find the best strategy for each player. Does this game have a saddle point? Is it a stable game?   Player 2 Strategy 1 2 3 Player 1 2 -1 -2 Soln:

Game Theory Solutions 5 For the game having the following payoff table, use the graphical procedure to determine the value of the game and the optimal mixed strategy for each player according to the minimax criterion.   Player 2 Strategy 1 2 3 Player 1 2 4