I'm working on this problem and I am completely lost. There there anyone out there that can help me. I see the problem worked out in the book, but I don't see how they obtained the numbers. Here is the problem

A decision maker who is considered to be a risk taker is faced with this set of probabilities and payoffs.

s1 s2 s3
d1 5 10 20
d2 -25 0 50
d3 -50 -10 80
probability .30 .35 .35

For the lottery p(80) + (1 - p)(-50), this decision maker has assessed the following indifference probabilities.

Payoff Probability
50 .60
20 .35
10 .25
5 .22
0 .20
-10 .18
-25 .10

Rank the decision alternatives on the basis of expected value and on the basis of expected utility.

Stacey,

I really don't have enough background in decision theory.....

The expected value for each decision alternative is pretty straightforward:

EV(d1) = (5*.30) + (10*.35) +(20*.35)

follow the same pattern for d2 and d3, and you'll see that d1 has the highest EV, followed by d2 and then d3

Since the person is a risk-taker (the higher the potential payoff, the more utility it has for them...), that implies that d3 may be the most attractive alternative, followed by d2, and then d1.

As far as using the indifference probabilities in computing expected utilities, I'm afraid I can't help much there....

Does the book have a good explanation of how to take the indifference probabilities* and use them to construct expected utilities?

*am I correct in interpreting that these? - for example, with payoff 50 and probability 0.60, this means that if the person thinks there'e a 60% chance of winning 50, the he/she will "play the game"

John

No the book doesn't. I spent a long time coming up with this:
EV=.60(80) + .40(-50)
48-20=28
EV=.35(80) + .65(-50)
28-32.5=-4.5
EV=.25(80) + .75(-50)
20-37.5= -17.5
EV=.22(80) + .78(-50)
17.6—39= -21.4
EV=.20(80) + .80(-50)
16- 40=-24
EV=.18(80) + .82(-50)
14.4 - -41= -26.6
EV=.10(80) + .90(-50)
8-45= -37
Then realized I wasn't getting the answers I needed.

Ugh! I will be glad when this class is over.

Yes you are right on the probability part...the way I understand it anyway.

I found this link - it may help....good luck

http://home.ubalt.edu/ntsbarsh/opre640a/partIX.htm#rutility