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 $₁ $2 $3 230 80 5 80 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) =

The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. Decision Alternative d₁ d₂ = EV(d₁) EV(d₂) The optimal decision is ? States of Nature $1 $2 230 80 $3 80 5 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. 80 55

The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives. Decision Alternative State of Nature 51 d₂ d2 (a) Use graphical sensitivity analysis to determine the range of probabilities of state of nature s, for which each of the decision alternatives has the largest expected value. d: is optimal for p(s₂) ≤ 0.2857 ; d. ✓ is optimal for p(s₂) > 0.2857 12 52 6 3 5 (b) Suppose P(s) = 0.2 and P(5₂) = 0.8. What is the best decision using the expected value approach? The best decision is d: with an expected value of 5.2 (c) Perform sensitivity analysis on the payoffs for decision alternative d₁. Assume the probabilities are as given in part (b), and find the range of payoffs under states of natures, and s₂ that will keep the solution found in part (b) optimal. As long as the payoff for s, is --?-- , then d₂ will be optimal. As long as the payoff for s₂ is --?-- Is the solution more sensitive to the payoff under state of nature…

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.

Suppose the equilibrium price for good quality used cars is $20,000. And the equilibrium price for poor quality used cars is $10,000. Assume a potential used car buyer has imperfect information as to the condition of any given used car. Assume this potential buyer believes the probability a given used car is good quality is .60 and the probability a given used car is low quality is .40. Assume the seller has perfect information on all cars in inventory. If the seller sells the buyer a good quality car, what is the net-benefit to the seller? a. A net gain of $4,000. b. A net gain of $20,000. c. A net loss of $4,000. d. A net loss of $10,000.

Consider the decision tree involving COSTS below. 300 0.6 0.4 500 1 500 0.7 0.3 200 Which of the following is true? O Action A should be chosen according to an expected value criterion. Action B should be chosen according to an expected value criterion. O Action A is a Nash equilibrium. O Action B is a Berge equilbrium.

Problem #4 - Jasper Inc. would like you to provide consulting services and provide recommendation on building a new assembly facility for air conditioning units in Florida. Jasper's initial assessment indicates the following conditions for this decision-making problem: With a favorable market in Florida, Jasper thinks that a large facility would result in a net profit of $200,000 to his firm. If the market is unfavorable in Florida, the construction of a large facility would result in $190,000 net loss. - A small facility would result in a net profit of $100,000 in a favorable market, but a net loss of $20,000 would occur if the market was unfavorable. Doing nothing would result in $0 profit in either market conditions. a) Create a decision table for this problem. b) What is your recommendation if y would apply the Maximax criterion (Optimistic)? C What is your recommendation if you would apply the Criterion of Realism (Hurwicz Criterion) with a erricient of realism a = 0.9? d) What is…