Handling Uncertainty. Ender Ozcan given by Peter Blanchfield
|
|
- Martin Harrell
- 5 years ago
- Views:
Transcription
1 Handling Uncertainty Ender Ozcan given by Peter Blanchfield
2 Objectives Be able to construct a payoff table to represent a decision problem. Be able to apply the maximin and maximax criteria to the table. Be able to apply the expected monetary value (EMV) criterion to the table. Be able to discuss the rationale, the strengths and the limitations of these criteria. 2
3 Introduction Many decisions are made under conditions of uncertainty, i.e. having made a decision you cannot be sure what the outcome will be. In this session, we will look at three simple criteria that can be used to help people facing decisions of this sort. We will also show how some problems can be represented as decision tables 3
4 Expected values These will underpin many of the methods that we will be applying to decision problems. An expected value (of X) is a long run average result. E X = Where p i is the probability of observation x i occurring For example for throwing a fair six sided dice a number of times - where the probability of any given number is 1/6 and assuming the numbers on the dice are 1, 2, 3 6 then E(x) is 21/6 or 3.5 the average of the six numbers i p i x i 4
5 Roulette A US roulette wheel has 38 equally likely outcomes. (p i = 1/38 for each number) A winning bet placed on a single number pays 35-to-1 (this means that you are paid 35 times your bet and your bet is returned, so you get 36 times your bet). What is the expected outcome of placing a $1 bet on any number? The outcome you loose will have a probability of 37/38 The outcome for these possibilities is -$1 you lose your money The outcome of winning is $36 5
6 Outcome of Roulette E(x) = (p lose. x lose ) + (p win. x win ) E(x) = (37/38. -$1) + (1/38 $36) = -$0.03 The bank will win! don t gamble on roulette 6
7 Business Example A sales person is paid commission on sales If the following sales commission has the given probability $80 probability 0.3 $90 probability 0.5 $100 probability 0.2 What is the sales person s expected outcome? 7
8 Decisions under uncertainty A company supplying paint to the car industry It has to buy the paint in on the probability it will be sold Otherwise they have a surplus to store, which costs them money Or they will not meet demand, which means the companies go elsewhere in future Daily demand for a given colour is for 1, 2 or 3 batches Any left over at the end of the day will cost $10 to store However each batch sells for $1000 and costs $500 Not having a batch will make future loss of $1000 per batch 8
9 The company s problem How many batches should they buy every day? We can work out a pay off table Demand Decision One Batch Two Batches Three Batches One batch $500 $0 -$500 Two batches $490 $1000 $500 Three batches $480 $500 $1500 9
10 The decision This will depend on the company strategy Pessimistic called maximin The worst outcome will always happen So choose the strategy with the best worst outcome In this case buying three batches has a worst outcome of making $480 profit 10
11 The Optimist The optimist always assumes the best possible outcome - MaxiMax In this case still buy three batches as they will make $
12 The realist - Expected monetary value (EMV) criterion This strategy takes into account the probabilities of the different outcomes of the decisions. It involves calculating the expected payoff of each decision and then selecting the decision with the best expected payoff. Let us randomly select thr4ee probabilities of the events Demand for 1 batch probability 0.3 Demand for 2 batches probability 0.6 Demand for 3 batches probability
13 Realistically Probabilities applied One p = 0.3 Two p = 0.6 Three p = 0.1 Risk One $150 $0 -$50 $100 Two $147 $600 $50 $797 The winner Three $144 $300 $150 $594 13
14 Limitations of EMV Since an expected value represents the average payoff that will result if the decision was repeated a large number of times, would it be reasonable to apply it to a one-off decision? It does not take into account the attitude to risk of the decision-maker. Only one objective, maximising monetary returns, is assumed. Many decisions involve other less quantifiable factors such as reputation. A linear value function for money is assumed i.e. each extra $1 received brings the same increase in satisfaction to the decision-maker. Generally the probabilities and payoffs are rough estimates. 14
Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques
1 Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques Thompson Lumber is looking at marketing a new product storage sheds. Mr. Thompson has identified three decision options (alternatives)
More informationModule 15 July 28, 2014
Module 15 July 28, 2014 General Approach to Decision Making Many Uses: Capacity Planning Product/Service Design Equipment Selection Location Planning Others Typically Used for Decisions Characterized by
More informationDecision Making. D.K.Sharma
Decision Making D.K.Sharma 1 Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision
More informationMath 180A. Lecture 5 Wednesday April 7 th. Geometric distribution. The geometric distribution function is
Geometric distribution The geometric distribution function is x f ( x) p(1 p) 1 x {1,2,3,...}, 0 p 1 It is the pdf of the random variable X, which equals the smallest positive integer x such that in a
More informationDECISION MAKING. Decision making under conditions of uncertainty
DECISION MAKING Decision making under conditions of uncertainty Set of States of nature: S 1,..., S j,..., S n Set of decision alternatives: d 1,...,d i,...,d m The outcome of the decision C ij depends
More informationDr. Abdallah Abdallah Fall Term 2014
Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Decision analysis Fundamentals of decision theory models Ch. 3 2 Decision theory Decision theory is an analytic and systemic way to tackle problems
More informationDecision Theory. Mário S. Alvim Information Theory DCC-UFMG (2018/02)
Decision Theory Mário S. Alvim (msalvim@dcc.ufmg.br) Information Theory DCC-UFMG (2018/02) Mário S. Alvim (msalvim@dcc.ufmg.br) Decision Theory DCC-UFMG (2018/02) 1 / 34 Decision Theory Decision theory
More informationDecision Analysis under Uncertainty. Christopher Grigoriou Executive MBA/HEC Lausanne
Decision Analysis under Uncertainty Christopher Grigoriou Executive MBA/HEC Lausanne 2007-2008 2008 Introduction Examples of decision making under uncertainty in the business world; => Trade-off between
More informationTECHNIQUES FOR DECISION MAKING IN RISKY CONDITIONS
RISK AND UNCERTAINTY THREE ALTERNATIVE STATES OF INFORMATION CERTAINTY - where the decision maker is perfectly informed in advance about the outcome of their decisions. For each decision there is only
More informationCauses of Poor Decisions
Lecture 7: Decision Analysis Decision process Decision tree analysis The Decision Process Specify objectives and the criteria for making a choice Develop alternatives Analyze and compare alternatives Select
More information1.The 6 steps of the decision process are:
1.The 6 steps of the decision process are: a. Clearly define the problem Discussion and the factors that Questions influence it. b. Develop specific and measurable objectives. c. Develop a model. d. Evaluate
More informationThe Course So Far. Atomic agent: uninformed, informed, local Specific KR languages
The Course So Far Traditional AI: Deterministic single agent domains Atomic agent: uninformed, informed, local Specific KR languages Constraint Satisfaction Logic and Satisfiability STRIPS for Classical
More informationFull file at CHAPTER 3 Decision Analysis
CHAPTER 3 Decision Analysis TRUE/FALSE 3.1 Expected Monetary Value (EMV) is the average or expected monetary outcome of a decision if it can be repeated a large number of times. 3.2 Expected Monetary Value
More informationexpected value of X, and describes the long-run average outcome. It is a weighted average.
X The mean of a set of observations is their ordinary average, whereas the mean of a random variable X is an average of the possible values of X The mean of a random variable X is often called the expected
More informationThe Course So Far. Decision Making in Deterministic Domains. Decision Making in Uncertain Domains. Next: Decision Making in Uncertain Domains
The Course So Far Decision Making in Deterministic Domains search planning Decision Making in Uncertain Domains Uncertainty: adversarial Minimax Next: Decision Making in Uncertain Domains Uncertainty:
More informationDecision Making. DKSharma
Decision Making DKSharma Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making
More informationMA 1125 Lecture 14 - Expected Values. Wednesday, October 4, Objectives: Introduce expected values.
MA 5 Lecture 4 - Expected Values Wednesday, October 4, 27 Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationChance/Rossman ISCAM II Chapter 0 Exercises Last updated August 28, 2014 ISCAM 2: CHAPTER 0 EXERCISES
ISCAM 2: CHAPTER 0 EXERCISES 1. Random Ice Cream Prices Suppose that an ice cream shop offers a special deal one day: The price of a small ice cream cone will be determined by rolling a pair of ordinary,
More informationDecision Analysis. Chapter Topics
Decision Analysis Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility Decision Analysis
More informationHOW TO BE SUCCESSFUL IN BINARY OPTION TRADING
HOW TO BE SUCCESSFUL IN BINARY OPTION TRADING Author William Morris www.binaryminimumdeposit.com Contents: INTRODUCTION 1 BINARY OPTIONS TRADING TIPS 2 Understand the Binary Options Market and Trading
More informationDecision Making. BUS 735: Business Decision Making and Research. Learn how to conduct regression analysis with a dummy independent variable.
Making BUS 735: Business Making and Research 1 Goals of this section Specific goals: Learn how to conduct regression analysis with a dummy independent variable. Learning objectives: LO5: Be able to use
More informationJohan Oscar Ong, ST, MT
Decision Analysis Johan Oscar Ong, ST, MT Analytical Decision Making Can Help Managers to: Gain deeper insight into the nature of business relationships Find better ways to assess values in such relationships;
More informationSubject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10.
e-pg Pathshala Subject : Computer Science Paper: Machine Learning Module: Decision Theory and Bayesian Decision Theory Module No: CS/ML/0 Quadrant I e-text Welcome to the e-pg Pathshala Lecture Series
More informationMean, Variance, and Expectation. Mean
3 Mean, Variance, and Expectation The mean, variance, and standard deviation for a probability distribution are computed differently from the mean, variance, and standard deviation for samples. This section
More informationIntroduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company
Valua%on and pricing (November 5, 2013) Lecture 4 Decision making (part 1) Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com LEARNING OBJECTIVES 1. List the steps of the decision-making
More informationDecision Analysis. Chapter Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall
Decision Analysis Chapter 12 12-1 Chapter Topics Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility
More informationNext Year s Demand -Alternatives- Low High Do nothing Expand Subcontract 40 70
Lesson 04 Decision Making Solutions Solved Problem #1: see text book Solved Problem #2: see textbook Solved Problem #3: see textbook Solved Problem #6: (costs) see textbook #1: A small building contractor
More informationKey concepts: Certainty Equivalent and Risk Premium
Certainty equivalents Risk premiums 19 Key concepts: Certainty Equivalent and Risk Premium Which is the amount of money that is equivalent in your mind to a given situation that involves uncertainty? Ex:
More informationDecision Making Supplement A
Decision Making Supplement A Break-Even Analysis Break-even analysis is used to compare processes by finding the volume at which two different processes have equal total costs. Break-even point is the
More informationDecision-making under conditions of risk and uncertainty
Decision-making under conditions of risk and uncertainty Solutions to Chapter 12 questions (a) Profit and Loss Statement for Period Ending 31 May 2000 Revenue (14 400 000 journeys): 0 3 miles (7 200 000
More information19 Decision Making. Expected Monetary Value Expected Opportunity Loss Return-to-Risk Ratio Decision Making with Sample Information
19 Decision Making USING STATISTICS @ The Reliable Fund 19.1 Payoff Tables and Decision Trees 19.2 Criteria for Decision Making Maximax Payoff Maximin Payoff Expected Monetary Value Expected Opportunity
More informationEconomic Risk and Decision Analysis for Oil and Gas Industry CE School of Engineering and Technology Asian Institute of Technology
Economic Risk and Decision Analysis for Oil and Gas Industry CE81.9008 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department
More informationSCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT. BF360 Operations Research
SCHOOL OF BUSINESS, ECONOMICS AND MANAGEMENT BF360 Operations Research Unit 5 Moses Mwale e-mail: moses.mwale@ictar.ac.zm BF360 Operations Research Contents Unit 5: Decision Analysis 3 5.1 Components
More informationDecision Making. BUS 735: Business Decision Making and Research. exercises. Assess what we have learned. 2 Decision Making Without Probabilities
Making BUS 735: Business Making and Research 1 1.1 Goals and Agenda Goals and Agenda Learning Objective Learn how to make decisions with uncertainty, without using probabilities. Practice what we learn.
More informationHomework 9 (for lectures on 4/2)
Spring 2015 MTH122 Survey of Calculus and its Applications II Homework 9 (for lectures on 4/2) Yin Su 2015.4. Problems: 1. Suppose X, Y are discrete random variables with the following distributions: X
More informationDecision Analysis. Chapter 12. Chapter Topics. Decision Analysis Components of Decision Making. Decision Analysis Overview
Chapter Topics Components of Decision Making with Additional Information Chapter 12 Utility 12-1 12-2 Overview Components of Decision Making A state of nature is an actual event that may occur in the future.
More informationAgenda. Lecture 2. Decision Analysis. Key Characteristics. Terminology. Structuring Decision Problems
Agenda Lecture 2 Theory >Introduction to Making > Making Without Probabilities > Making With Probabilities >Expected Value of Perfect Information >Next Class 1 2 Analysis >Techniques used to make decisions
More informationLearning Objectives 6/2/18. Some keys from yesterday
Valuation and pricing (November 5, 2013) Lecture 12 Decisions Risk & Uncertainty Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.centime.biz Some keys from yesterday Learning Objectives v Explain
More informationChapter 18 Student Lecture Notes 18-1
Chapter 18 Student Lecture Notes 18-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 18 Introduction to Decision Analysis 5 Prentice-Hall, Inc. Chap 18-1 Chapter Goals After completing
More informationShould Win Limits Become a Part of Responsible Gambling?
Should Win Limits Become a Part of Responsible Gambling? Presented by Doug Walker College of Charleston Responsible Gambling Council Discovery 2017 20 April Toronto, Canada A typical casino visit Consider
More informationDecision making under uncertainty
Decision making under uncertainty 1 Outline 1. Components of decision making 2. Criteria for decision making 3. Utility theory 4. Decision trees 5. Posterior probabilities using Bayes rule 6. The Monty
More informationChoose between the four lotteries with unknown probabilities on the branches: uncertainty
R.E.Marks 2000 Lecture 8-1 2.11 Utility Choose between the four lotteries with unknown probabilities on the branches: uncertainty A B C D $25 $150 $600 $80 $90 $98 $ 20 $0 $100$1000 $105$ 100 R.E.Marks
More informationNotes for Session 2, Expected Utility Theory, Summer School 2009 T.Seidenfeld 1
Session 2: Expected Utility In our discussion of betting from Session 1, we required the bookie to accept (as fair) the combination of two gambles, when each gamble, on its own, is judged fair. That is,
More informationDecision Analysis REVISED TEACHING SUGGESTIONS ALTERNATIVE EXAMPLES
M03_REND6289_0_IM_C03.QXD 5/7/08 3:48 PM Page 7 3 C H A P T E R Decision Analysis TEACHING SUGGESTIONS Teaching Suggestion 3.: Using the Steps of the Decision-Making Process. The six steps used in decision
More informationDecision Making Models
Decision Making Models Prof. Yongwon Seo (seoyw@cau.ac.kr) College of Business Administration, CAU Decision Theory Decision theory problems are characterized by the following: A list of alternatives. A
More informationTextbook: pp Chapter 3: Decision Analysis
1 Textbook: pp. 81-128 Chapter 3: Decision Analysis 2 Learning Objectives After completing this chapter, students will be able to: List the steps of the decision-making process. Describe the types of decision-making
More informationSensitivity = NPV / PV of key input
SECTION A 20 MARKS Question One 1.1 The answer is D 1.2 The answer is C Sensitivity measures the percentage change in a key input (for example initial outlay, direct material, direct labour, residual value)
More informationChapter 3. Decision Analysis. Learning Objectives
Chapter 3 Decision Analysis To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationTRINITY COLLGE DUBLIN
TRINITY COLLGE DUBLIN School of Computer Science and Statistics Extra Questions ST3009: Statistical Methods for Computer Science NOTE: There are many more example questions in Chapter 4 of the course textbook
More informationExpectation Exercises.
Expectation Exercises. Pages Problems 0 2,4,5,7 (you don t need to use trees, if you don t want to but they might help!), 9,-5 373 5 (you ll need to head to this page: http://phet.colorado.edu/sims/plinkoprobability/plinko-probability_en.html)
More informationApplying Risk Theory to Game Theory Tristan Barnett. Abstract
Applying Risk Theory to Game Theory Tristan Barnett Abstract The Minimax Theorem is the most recognized theorem for determining strategies in a two person zerosum game. Other common strategies exist such
More informationDecision Analysis. Introduction. Job Counseling
Decision Analysis Max, min, minimax, maximin, maximax, minimin All good cat names! 1 Introduction Models provide insight and understanding We make decisions Decision making is difficult because: future
More informationExpected value is basically the average payoff from some sort of lottery, gamble or other situation with a randomly determined outcome.
Economics 352: Intermediate Microeconomics Notes and Sample Questions Chapter 18: Uncertainty and Risk Aversion Expected Value The chapter starts out by explaining what expected value is and how to calculate
More informationPhil 321: Week 2. Decisions under ignorance
Phil 321: Week 2 Decisions under ignorance Decisions under Ignorance 1) Decision under risk: The agent can assign probabilities (conditional or unconditional) to each state. 2) Decision under ignorance:
More informationHeckmeck am Bratwurmeck or How to grill the maximum number of worms
Heckmeck am Bratwurmeck or How to grill the maximum number of worms Roland C. Seydel 24/05/22 (1) Heckmeck am Bratwurmeck 24/05/22 1 / 29 Overview 1 Introducing the dice game The basic rules Understanding
More informationObtaining a fair arbitration outcome
Law, Probability and Risk Advance Access published March 16, 2011 Law, Probability and Risk Page 1 of 9 doi:10.1093/lpr/mgr003 Obtaining a fair arbitration outcome TRISTAN BARNETT School of Mathematics
More informationRandom variables. Discrete random variables. Continuous random variables.
Random variables Discrete random variables. Continuous random variables. Discrete random variables. Denote a discrete random variable with X: It is a variable that takes values with some probability. Examples:
More informationPart 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?
1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard
More informationAmbiguity Aversion. Mark Dean. Lecture Notes for Spring 2015 Behavioral Economics - Brown University
Ambiguity Aversion Mark Dean Lecture Notes for Spring 2015 Behavioral Economics - Brown University 1 Subjective Expected Utility So far, we have been considering the roulette wheel world of objective probabilities:
More informationSTA 103: Final Exam. Print clearly on this exam. Only correct solutions that can be read will be given credit.
STA 103: Final Exam June 26, 2008 Name: } {{ } by writing my name i swear by the honor code Read all of the following information before starting the exam: Print clearly on this exam. Only correct solutions
More informationChapter 2 supplement. Decision Analysis
Chapter 2 supplement At the operational level hundreds of decisions are made in order to achieve local outcomes that contribute to the achievement of the company's overall strategic goal. These local outcomes
More informationLearning Objectives = = where X i is the i t h outcome of a decision, p i is the probability of the i t h
Learning Objectives After reading Chapter 15 and working the problems for Chapter 15 in the textbook and in this Workbook, you should be able to: Distinguish between decision making under uncertainty and
More informationMLLunsford 1. Activity: Mathematical Expectation
MLLunsford 1 Activity: Mathematical Expectation Concepts: Mathematical Expectation for discrete random variables. Includes expected value and variance. Prerequisites: The student should be familiar with
More informationSTAT 3090 Test 2 - Version B Fall Student s Printed Name: PLEASE READ DIRECTIONS!!!!
Student s Printed Name: Instructor: XID: Section #: Read each question very carefully. You are permitted to use a calculator on all portions of this exam. You are NOT allowed to use any textbook, notes,
More informationstake and attain maximum profitability. Therefore, it s judicious to employ the best practices in
1 2 Success or failure of any undertaking mainly lies with the decisions made in every step of the undertaking. When it comes to business the main goal would be to maximize shareholders stake and attain
More informationDecision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:
CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.
More informationInformation Technology Project Management, Sixth Edition
Management, Sixth Edition Prepared By: Izzeddin Matar. Note: See the text itself for full citations. Understand what risk is and the importance of good project risk management Discuss the elements involved
More informationNotes 10: Risk and Uncertainty
Economics 335 April 19, 1999 A. Introduction Notes 10: Risk and Uncertainty 1. Basic Types of Uncertainty in Agriculture a. production b. prices 2. Examples of Uncertainty in Agriculture a. crop yields
More informationSubjective Expected Utility Theory
Subjective Expected Utility Theory Mark Dean Behavioral Economics Spring 2017 Introduction In the first class we drew a distinction betweem Circumstances of Risk (roulette wheels) Circumstances of Uncertainty
More informationIX. Decision Theory. A. Basic Definitions
IX. Decision Theory Techniques used to find optimal solutions in situations where a decision maker is faced with several alternatives (Actions) and an uncertain or risk-filled future (Events or States
More informationChapter 13 Decision Analysis
Problem Formulation Chapter 13 Decision Analysis Decision Making without Probabilities Decision Making with Probabilities Risk Analysis and Sensitivity Analysis Decision Analysis with Sample Information
More informationP1 Performance Operations
Operational Level Paper P1 Performance Operations Examiner s Answers SECTION A Answer to Question One 1.1 The correct answer is D. 1.2 $40,000 x 3.791 = $151,640 $50,000 / $151,640 = 0.3297 = 33.0% The
More informationLecture 11: Critiques of Expected Utility
Lecture 11: Critiques of Expected Utility Alexander Wolitzky MIT 14.121 1 Expected Utility and Its Discontents Expected utility (EU) is the workhorse model of choice under uncertainty. From very early
More informationDECISION ANALYSIS: INTRODUCTION. Métodos Cuantitativos M. En C. Eduardo Bustos Farias 1
DECISION ANALYSIS: INTRODUCTION Cuantitativos M. En C. Eduardo Bustos Farias 1 Agenda Decision analysis in general Structuring decision problems Decision making under uncertainty - without probability
More informationManagerial Economics
Managerial Economics Unit 9: Risk Analysis Rudolf Winter-Ebmer Johannes Kepler University Linz Winter Term 2015 Managerial Economics: Unit 9 - Risk Analysis 1 / 49 Objectives Explain how managers should
More informationMartingales. Will Perkins. March 18, 2013
Martingales Will Perkins March 18, 2013 A Betting System Here s a strategy for making money (a dollar) at a casino: Bet $1 on Red at the Roulette table. If you win, go home with $1 profit. If you lose,
More informationChapter 7. Random Variables
Chapter 7 Random Variables Making quantifiable meaning out of categorical data Toss three coins. What does the sample space consist of? HHH, HHT, HTH, HTT, TTT, TTH, THT, THH In statistics, we are most
More informationReview of Expected Operations
Economic Risk and Decision Analysis for Oil and Gas Industry CE81.98 School of Engineering and Technology Asian Institute of Technology January Semester Presented by Dr. Thitisak Boonpramote Department
More informationManagerial Economics Uncertainty
Managerial Economics Uncertainty Aalto University School of Science Department of Industrial Engineering and Management January 10 26, 2017 Dr. Arto Kovanen, Ph.D. Visiting Lecturer Uncertainty general
More informationMaximizing Winnings on Final Jeopardy!
Maximizing Winnings on Final Jeopardy! Jessica Abramson, Natalie Collina, and William Gasarch August 2017 1 Introduction Consider a final round of Jeopardy! with players Alice and Betty 1. We assume that
More informationConcave utility functions
Meeting 9: Addendum Concave utility functions This functional form of the utility function characterizes a risk avoider. Why is it so? Consider the following bet (better numbers than those used at Meeting
More informationECON Microeconomics II IRYNA DUDNYK. Auctions.
Auctions. What is an auction? When and whhy do we need auctions? Auction is a mechanism of allocating a particular object at a certain price. Allocating part concerns who will get the object and the price
More informationFundamentals Level Skills Module, Paper F5. 1 Cement Co. (a)
Answers Fundamentals Level Skills Module, Paper F5 Performance Management June 2011 Answers 1 Cement Co (a) Pay off table SUPPLY (no. of bags) Prob.* 350,000 280,000 200,000 Weather $ 000 $ 000 $ 000 Good
More informationM G T 2251 Management Science. Exam 3
M G T 2251 Management Science Exam 3 Professor Chang November 8, 2012 Your Name (Print): ID#: Read each question carefully before you answer. Work at a steady pace, and you should have ample time to finish.
More informationMgtOp 470 Business Modeling with Spreadsheets Washington State University Sample Final Exam
MgtOp 470 Business Modeling with Spreadsheets Washington State University Sample Final Exam Section 1 Multiple Choice 1. An information desk at a rest stop receives requests for assistance (from one server).
More information1. better to stick. 2. better to switch. 3. or does your second choice make no difference?
The Monty Hall game Game show host Monty Hall asks you to choose one of three doors. Behind one of the doors is a new Porsche. Behind the other two doors there are goats. Monty knows what is behind each
More informationmon ey (m¾n ) n. , pl.
1 mon ey (m¾n ) n., pl. mon eys or mon ies. 1. A commodity, such as gold, or an officially issued coin or paper note that is legally established as an exchangeable equivalent of all other commodities,
More informationModels & Decision with Financial Applications Unit 3: Utility Function and Risk Attitude
Models & Decision with Financial Applications Unit 3: Utility Function and Risk Attitude Duan LI Department of Systems Engineering & Engineering Management The Chinese University of Hong Kong http://www.se.cuhk.edu.hk/
More informationDecision Analysis CHAPTER 19 LEARNING OBJECTIVES
CHAPTER 19 Decision Analysis LEARNING OBJECTIVES This chapter describes how to use decision analysis to improve management decisions, thereby enabling you to: 1. Make decisions under certainty by constructing
More informationDay Trading Smart Right From the Start. David Nassar
Day Trading Smart Right From the Start David Nassar David S. Nassar President/CEO Market Wise Securities, Inc. Member NASD-SIPC, Twelve Years Award-Winning Securities Experience Published Best Selling
More informationMaximizing Winnings on Final Jeopardy!
Maximizing Winnings on Final Jeopardy! Jessica Abramson, Natalie Collina, and William Gasarch August 2017 1 Abstract Alice and Betty are going into the final round of Jeopardy. Alice knows how much money
More informationOutline. Decision Making Theory and Homeland Security. Readings. AGEC689: Economic Issues and Policy Implications of Homeland Security
Decision Making Theory and Homeland Security AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong Jin AGEC689: Economic Issues and Policy Implications of Homeland Security Yanhong
More informationBRIEF INTRODUCTION TO GAME THEORY
BRIEF INTRODUCTION TO GAME THEORY Game Theory Mathematical theory that deals with the general features of competitive situations. Examples: parlor games, military battles, political campaigns, advertising
More information05/05/2011. Degree of Risk. Degree of Risk. BUSA 4800/4810 May 5, Uncertainty
BUSA 4800/4810 May 5, 2011 Uncertainty We must believe in luck. For how else can we explain the success of those we don t like? Jean Cocteau Degree of Risk We incorporate risk and uncertainty into our
More informationC7: Quantitative Techniques
COURSE MANUAL C7 Quantitative Techniques Module 5 [Add institute name here] [Add School/Department name here] Copyright Commonwealth of Learning 2012 All rights reserved. No part of this course may be
More informationUsing the Maximin Principle
Using the Maximin Principle Under the maximin principle, it is easy to see that Rose should choose a, making her worst-case payoff 0. Colin s similar rationality as a player induces him to play (under
More informationGEK1544 The Mathematics of Games Suggested Solutions to Tutorial 3
GEK544 The Mathematics of Games Suggested Solutions to Tutorial 3. Consider a Las Vegas roulette wheel with a bet of $5 on black (payoff = : ) and a bet of $ on the specific group of 4 (e.g. 3, 4, 6, 7
More informationEngineering Risk Benefit Analysis
Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ES.72, ES.721 A 1. The Multistage ecision Model George E. Apostolakis Massachusetts Institute of Technology
More informationEcon 323 Microeconomic Theory. Practice Exam 2 with Solutions
Econ 323 Microeconomic Theory Practice Exam 2 with Solutions Chapter 10, Question 1 Which of the following is not a condition for perfect competition? Firms a. take prices as given b. sell a standardized
More informationPaper P1 Performance Operations Russian Diploma Post Exam Guide November 2012 Exam. General Comments
General Comments This paper was generally well attempted by candidates, as evidenced by the overall pass rate. The one question which posed a significant challenge was Question 3, where candidates had
More information