expected utility and expected value + diagrams - BUS221

EV Formula

EV= (P1 xV1) + (P2 x V2)....+ (pn x vn)

P= Probability
V=Value

Expected utility formula

EU= (P1 x U1) + (P2 x U2) +.......+ (Pn x n)

P- probability
U= Utility

Sylvester wants to try a new dish at Romeo’s Restaurant. His choices are: the eggplant soufflé, the vegan stir-fry or the fried octopus.

He knows that no matter what he picks, he will either enjoy it or not enjoy it.

What are the possible outcomes for Sylvester?

Maria is going to the park to meet her friend Kenji. She has just styled her hair and does not want it to get wet. She must decide whether or not to take an umbrella with her. If it rains, Maria wants to have the umbrella, but if it is sunny she does not want to carry the
umbrella.

What are Maria’s possible outcomes?

Action 1 will provide a utility of 5 if state “p” occurs and 6 if state “n” occurs.

Action 2 will provide a utility of 8 under state “p” and 1 under state “n”. The probability of state “p” is 60% and the probably of state “n” is 40%.

What is the expected utility of Action 1 and Action 2 (Round to the nearest tenth)?

Action 1 will provide a utility of 7 if state “p” occurs and 3 if state “n” occurs. Action 2 will provide a utility of 5 under state “p” and 4 under state “n”. The probability of state “p” is 55% and the probably of state “n” is 45%.

What is the expected utility of Action 1 and Action 2 (Round to the nearest tenth)?

Action 1 will provide a utility of 9 if state “p” occurs and 1 if state “n” occurs. Action 2
will provide a utility of 5 under state “p” and 8 under state “n”. The probability of state
“p” is 10% and the probably of state “n” is 90%. What is the expected utility of Action 1
and Action 2 (Round to the nearest tenth)?

Action 1 will provide a utility of 4 if state “p” occurs and 2 if state “n” occurs. Action 2
will provide a utility of 1 under state “p” and 10 under state “n”. The probability of state
“p” is 95% and the probably of state “n” is 5%. What is the expected utility of Action 1
and Action 2 (Round to the nearest tenth)?

Action 1 will provide a utility of 5 if state “p” occurs and 4 if state “n” occurs. Action 2
will provide a utility of 8 under state “p” and 3 under state “n”. The probability of state
“p” is 30%. If “p” doesn’t occur, “n” will. What is the expected utility of Action 1 and
Action 2 (Round to the nearest tenth)?

Zach is looking to get his car repaired.

due to a change in management, their quality has gone down and he only receives a utility of 6 when he brings his car there.

The first is an expensive, top-of-the-line shop

• Chances that Zach will be dissatisfied (utility of 1) are 0% with this shop.

• The probability that the job will be of the same quality as the go-to shop is 30%;

• — more expensive- Zach will only get a utility of 5

• If the job is done exceptionally well, Zach will get a utility of 9.

The other company offers better prices.

• dissatisfaction (utility 1) seems to be around 25%, based on what he’s heard about the place.

• The chances that they will do an average job (utility of 6) are 65%.

• However, if they do an exceptional job at a lower price, Zach will experience a utility of 10

Calculate the expected utility of the 3 shops. Use decision theory to give a reasoned recommendation to Zach.

Khalid is trying to decide what to do on a Saturday night. He usually goes clubbing, but today he’s been invited to a boardgame night by some friends. He likes boardgames and this is a good group, so he thinks going would be quite fun. Unless, of course, Ian shows
up. Khalid absolutely hates spending time with Ian. Going to the club is probably going to be fun, but not as fun as a boardgame night without Ian. There is, however, the chance that this would be one of those “magical” nights at the club that happen every so often.
Those, to Khalid, are the absolute best way of spending a Saturday night.

Assign plausible utility numbers to each of the outcomes described in this scenario.

• Assume there is a 10% chance that Ian will be at the boardgame night

• there is a 5% chance that the night at the club will be “magical”.

What is the expected utility of going to the club and what is the expected utility of going to the boardgame night?

Priya is deciding where to go for lunch. She typically eats at the campus cafeteria, but today her colleague invited her to try a new ramen restaurant nearby. She enjoys ramen and likes her colleague's company, so she thinks going would be quite enjoyable. Unless, of course, the restaurant is crowded with a long wait. Priya strongly dislikes waiting in lines. Eating at the cafeteria is generally satisfactory, but not as satisfying as a peaceful meal at the ramen place. There is, however, the possibility that the cafeteria will be serving her favorite dish today, which happens occasionally.

Those days, for Priya, provide the most enjoyable lunch experience possible.

Assign plausible utility numbers to each of the outcomes described in this scenario.

• Assume there is a 30% chance that the ramen restaurant will be crowded,

• 15% chance that the cafeteria will be serving Priya's favorite dish.

• What is the expected utility of going to the cafeteria and what is the expected utility of going to the ramen restaurant?