Assignment 4 – Utility Theory and Game Theory Due: Oct 13, 2021 Complete the assignment questions using Microsoft Word, Microsoft Excel, or a combination of both. You may draw decision trees by hand. Question #Points142939Excel Bonus1Total23 Notes: To get the Excel bonus for this assignment, you must draw your utility curves for problems 1a and 2e in Excel by using Excel’s graphing capability.You may upload 2 files for your submission: 1 Excel file and 1 Word file. Best of Luck 😊 Question 1: In chapter 3, a decision tree was developed for John Thompson (see Figure below). The decision tree analysis recommended that John conduct the market survey. If the survey results are favourable, the recommended alterative is Large Plant. If the survey results are negative, the recommended alternative is Small Plant. After completing the analysis, John was not completely sure that he is indifferent to risk. He wants the analysis completed over again with his risk tolerance taken into consideration. After going through a number of standard gambles, John was able to assess his utility for money. Here are some of the utility assessments: U(−$190,000)=0U(−$20,000)=0.15U($90,000)= 0.5U($200,000)=1.0U(−$180,000)=0.05U(−$10,000)=0.2U($100,000)=0.6 U(−$30,000)=0.10U($0)=0.3U($190,000)=0.95 Draw a Utility Curve for John’s preference for money. (2 points)If John maximizes his expected utility (instead of maximizing EMV), does his decision change? Show your calculations. (2 points) Question 2: Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested that Jim use either a survey or a pilot study to test the market. The survey would be a sophisticated questionnaire administered to a test market. It will cost $5,000. Another alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron Bush has suggested that it would be a good idea for Jim to conduct either the survey or the pilot before Jim makes the decision concerning whether to produce the new razor. But Jim is not sure if the value of the survey or the pilot is worth the cost. Jim estimates that the probability of a successful market without performing a survey or pilot study is 0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7, and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study given an unfavorable market is 0.9, and the probability of an unsuccessful pilot study result given a favorable market for razors is 0.2. Draw the decision tree for this problem without the probability values. (2 points)Compute the revised probabilities needed to complete the decision, and place these values in the decision tree. Show your calculations. (2 points)What is the best decision for Jim? Use EMV as the decision criterion. Show your calculations. (2 points) Jim Sellers has been able to estimate his utility for a number of different values. He would like to use these utility values in making the decision. U(−$80,000)=0U(−$20,000)=0.7U($80,000)= 0.9U(−$65,000)=0.5U(−$5,000)=0.8U($95,000)=0.95U(−$60,000)=0.55U($0)=0.81U($100,000)=1.0 Resolve the problem using utility values. Show your calculations. (2 points)Is Jim a risk avoider? Hint: Draw Jim’s utility curve. (1 point) Question 3: What is the value of the following game and the strategies for A and B? (2 points) B1B2A11920A25-4 What is the value of the following game? (3 points) S1S2R121116R2893 Solve the following game? (4 points) Y1Y2X1-5-10X2128X3412X4-40-5
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