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# Decision Making Under Risk - Expected Payoff

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CoffeeTime is considering selling juices along with its other products.
States of Nature
High Sales Med. Sales Low Sales
A(0.2) B(0.5) C(0.3)
A1 (sell juices) 3000 2000 -6000
A2 (don't sell juices) 0 0 0
The probabilities shown above represent the states of nature and the decision maker's (e.g., manager) degree of uncertainties and personal judgment on the occurrence of each state. What is the expected payoff for actions A1 and A2 above? What would be your recommendation? Interpret the results based on practical considerations.
b. Bayes and empirical Bayes (EB) methods structure combining information from similar components of information and produce efficient inferences for both individual components and shared model characteristics. For example, city-specific information on the profits involved in selling a particular brand of coffee in Mumbai might be unavailable. How could CoffeeTime "borrow information" from adjacent cities or other countries to employ Bayesian logic?
Finally, what additional strategy (or variation on a given strategy) would you recommend to the key decision maker to solve the challenge given? Prepare a 350-word memo to the simulation's key decision maker advocating your recommendation.

https://brainmass.com/economics/uncertainty/decision-making-risk-expected-payoff-63885

#### Solution Preview

Please see the attached file for complete solution. Thanks

a.
Expected payoff = SPi*Xi
Where Pi=Probability of state of nature i
Xi=payoff under state of nature I
Expected payoff A1 = 0.2*3000+0.5*2000+0.3*(-6000) = -200
Expected payoff A2 = 0.2*0+0.5*0+0.3*0 = 0

What would be your recommendation? Interpret the results based on practical considerations.
As the expected payoff is higher when the decision for not to sell juices is taken, I recommend a decision for not to sell juices.
The practical consideration is that if we decide to ...

#### Solution Summary

A simple and systematic way to show how decision-making can be done when choices are made under uncertainty. The concepts of probability and expected payoff are used to select the best alternative for the CoffeeTime. The post also discusses the practical considerations along with financial considerations while taking a decision. In the second part, it discusses how the city specific information on the profits can or cannot be used for taking decision in another city

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## Decision Analysis Questions

All questions have been answered. I just need someone to check the accuracy of my answers.

Thank you.

True/False

Indicate whether the sentence or statement is true or false.

T 1. A state of nature is an actual event that may occur in the future.

F 2. The maximin criterion results in the maximum of the maximum payoffs.

F 3. The Hurwicz criterion is a compromise between the maximax and maximin criteria.

T 4. The minimax regret criterion maximizes the maximum regret.

F 5. The Hurwicz criterion multiplies the worst payoff by the coefficient of optimism.

Multiple Choice

Identify the letter of the choice that best completes the statement or answers the question.

C 6. The maximax criterion results in the

a. minimum of the minimum payoffs

b. maximum of the minimum payoffs

c. maximum of the maximum payoffs

d. minimum of the maximum payoffs

A 7. The Hurwicz criterion multiplies the

a. best payoff by the coefficient of optimism

b. worst payoff by the coefficient of optimism

c. best payoff by the worst payoff

d. none of the above

C 8. The difference between expected payoff under certainty and expected payoff under risk is the

a.expected net value

b. expected rate of return

c. expected value of perfect information

d. expected value

C 9. Which of the following is not an approach for decision making under uncertainty?

a. minimax

b.maximin

c.decision tree

d.minimax regret

C 10. The ______________ of sample information is the ratio of the expected value of sample information to the expected value of perfect information

a. utilization

b. expected value

c. efficiency

d. coefficient

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