1. With the easing of COVID restrictions for indoor dining, and the return of tourists to a big city, Bridgette has decided to follow her love of gourmet cooking and invest in a small caf in a heavily touristed part of the city. After many conversations with her banker, her proposed chef, and forecasts of tourism, she came up with the following payoff table showing profit in $1000s for her share of the investment.

	Low	Medium	High
Small	50	60	75
Medium	30	60	100

a. What are the decision alternatives? How can you tell? b. What are the states of nature? How can you tell? c. Bridgette is an optimistic decision-maker. What decision would an optimistic decision- maker choose? State the criterion used ?

Cody is also interested in investing in this caf, but his decision-making criterion is 'minimax regret.' You are to help Cody figure out what decision to make using this criterion. The first step is to calculate the regret table, and then to take the minimum of the maxium regret for each decision (hence minimax regret). a. What is the highest possible profit for each state of nature in the table above?

b. Using your results from step A, calculate the regrets and give the regret table below c. Using your table in b, calculate the minimax regret and state what Cody's minimax regret decision is.

2. A startup tech company is planning to introduce a new device which it believes will be useful for both businesses and consumers. Ngoc, the product manager, came up with the following payoff table (in $millions . She knows that Mario, the company CEO follows a minimax regret criterion when making decisions, so she does that for him as well.

	Courses of action
Event	Market present design	do not market present design present
Introduction Succesful	$500	-$25
Introduction not successful	-$50	-$25

a. What are the decision alternatives? b. What are the states of nature?

c. What is the highest possible return for each state of nature. d. Show the regret table below. e. Calculate the minimax regret in the table above. What is the decision that Mario would make, based on Ngoc's calculations?

3. Cyrus's rich uncle died and left him a sizable inheritance. He thought about keeping his uncle's portfolio of investments just as he had left it since he ended up so rich, but Cyrus realized that since his uncle was an old man, he invested in more conservative instruments as he got older. Cyrus is young and optimistic, so he thought he might try a more aggressive portfolio, particularly investing in new technologies. His decision alternatives at this point are to keep the portfolio as is (D1), or to invest more aggressively (D2), even though that has greater risk, especially with the COVID pandemic lingering, inflation, and the war in Ukraine. He developed the following payoff table (in $1000s), with S1 and S2 the state of new technological developments being strong (S1) or weak (S2) in the coming year.

	Strong	Weak
Keep portfolio as is	70	30
Invest aggressievely	100	-20

a. Find the highest return for each state of nature. b. Calculate the regret table below. c. Use the table to calculate the minimax regret. What decision should Cyrus make?