roup of answer choices Amanda's preference is to visit Inverness If this is a sequential game and Bernardo can move first, Amanda's preference is to visit Perth. There are two Nash equilibria in this game If this is a one-shot, simultaneous game, then both players would choose Perth since it is the highest total payoff
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The below table shows a payoff matrix that represents the interaction between two friends, Amanda and Bernardo. They are deciding which city to visit together.
Bernardo | |||
Inverness | Perth | ||
Amanda | Inverness | 7, 4 | 2.5, 1 |
Perth | 1, 2.5 | 3, 9 |
Select all the correct answers.
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- 9. The East Chester Tribune must decide whether to publish a Sunday edition. The publisher thinks the probability is 0.6 that a Sunday edition would be a success and 0.4 that it would be a failure. If it is a success, she will gain $100,000. If it is a failure, she will lose $80,000. a. Construct a decision tree corresponding to the problem, and use backward induction to solve the problem. (Assume that the publisher is risk-neutral.) b. List all forks in the decision tree you constructed; then indicate whether each is a decision fork or a chance fork and state why.Many decision problems have the following simplestructure. A decision maker has two possible decisions,1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utility.The following payoff table shows a profit for a decision analysis problem with two decision alternatives and three states of nature. In order to get full credit, show your all work done step by step including cell calculations using excel functions. State of Nature Decion Alternatives s1 s2 s3 d1 250 100 50 d2 100 75 100 a) Construct a decision tree for this problem. b) Suppose that the decision-maker obtains the probabilities P(s1)=0.65, P(s2)=0.15, and P(s3)=0.20. Use the expected value approach to determine the optimal decision.
- The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ States of Nature 51 52 $3 230 80 5 80 80 55 Suppose that the decision maker obtained the probabilities P(5₁) = 0.65, P(S₂) = 0.15, and P(53) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₂) = EV(d₂) = The optimal decision is?.The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative = d₁ d₂ States of Nature 51 230 80 $2 $3 80 5 80 55 Suppose that the decision maker obtained the probabilities P(S₁) = 0.65, P(s₂) = 0.15, and P(S3) = 0.20. Use the expected value approach to determine the optimal decision. EV(d₁) EV(d₂)Peter Martin will help his brother who wants to open a grocery store. Peter initially believes there is a 50-50 chance that his brother's food store will be successful. Peter is considering doing market research. Based on historical data, there is a 0.8 probability that the market research will be favorable given a successful store. Furthermore, there is a 0.7 probability that the market research will be unfavorable given an unsuccessful store. a) If the market research is favorable, what is Peter's revised probability of a successful store for his brother?b) If the market survey is unfavorable, what is Peter's revised probability of a successful store for his brother?c) If the initial probability of a successful store is 0.60 (instead of 0.50), find the probabilities of (a) and (b).
- If you want to invest in a project that cost $3.5 million. As we are unsure about the future demand, there is a 40% probability of high demand with a present value for the project $3 million. There is a 25% probability of moderate demand with a present value of $2.5 million. In addition, there is a 35% probability of low demand with a present value is $1.5 million. Draw a decision tree for this problem. What is the expected net present value of the business? Should you invest? Explain. Assume that you can expand the project by investing another $0.6 million after you learn the true future demand state. This would make the present value of the business $3.9 million in the high‐demand state, $3.5 million in the moderate demand state, and $1.80 million in the low demand state. Draw a decision tree to reflect the option to expand. Evaluate the alternatives. What is the net present value of the business if you consider the option to expand? How valuable is the option to expand?The following payoff table shows the profit for a decision problem with two states of nature and three decision alternatives, Decision State of Nature Lternative s1 S2 D1 10 30 D2 -5 20 D3 60 -10 Identify the decision taken under the following approaches: (1) Pessimistic (2) Optimistic (3) Equal probability (4) Regret (5) Hurwicz criterion. Note : The decision maker's degree of optimism (a) being 0.6.A small strip-mining coal company is trying to decide whether it should purchase or lease a new clamshell. If purchased, the “shell” will cost $152,500 and is expected to have a $50,000 salvage value after 6 years. Alternatively, the company can lease a clamshell for only $16,000 per year, but the lease payment will have to be made at the beginning of each year. If the clamshell is purchased, it will be leased to other strip-mining companies whenever possible, an activity that is expected to yield revenues of $9,000 per year. If the company’s MARR is 13% per year, should the clamshell be purchased or leased on the basis of a future worth analysis? Assume the annual M&O cost is the same for both options. The future worth when purchased is $ The future worth when leased is $
- A company is considering a new product launch. There is a 0.6 chance that demand for the product will be strong and a 0.4 chance that demand will be weak. Two strategies for the launch are possible: 1 has high promotion costs and a net cash outflow of K120 000 if demand proves to be strong, and if demand proves weak a net cash outflow of (K30 000) will result. Strategy 2 has low promotion costs and if demand is strong will generate a cash inflow of only K80 000 but with weak demand a net cash inflow of K20 000. Draw a decision tree and advise which course of action generates the greatest expected profit. What is the maximum amount that should be paid for market research to determine with certainty whether demand will be strong or weak?Train an ID3 decision tree for a dataset shown in the following table. The table contains 2 categorical attributes (refund and marital status) and 1 continuous attribute (taxable income). Once you got the model then use it to classify the input X1 (No, Single, 95K) and X2 (Yes, Divorced, 120K) ID Marital Refund Тахable Cheat Status Income 1 Single Yes 125K No 2 Married No 100K No 3 Single No 70K No 4 Married Yes 120K No Divorced No 95K Yes Married No 60K No 7 Divorced Yes 220K No 8 Single No 85K Yes Married No 75K No 10 Single No 90K Yes 00The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ States of Nature 51 5₂ 53 260 110 35 110 110 85 The probabilities for the states of nature are P(S₁) = 0.65, P(S₂) = 0.15, and P(s) = 0.20. (a) What is the optimal decision strategy if perfect information were available? If s, then? ;If s₂ then 2 ✓; If s₂ then ? (b) What is the expected value for the decision strategy developed in part (a)? (c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value? The recommended decision without perfect information is ? EV = (d) What is the expected value of perfect information? EVPI =