Information Systems Engineering Prof. Yuval Shahar, M.D., Ph.D

פרופ' יובל שחר הנדסת מערכות מידע

Information Systems Engineering Prof. Yuval Shahar, M.D., Ph.D.

תרגיל 3

ניתוח וקבלת החלטות במערכות מידע

Judgment and Decision Making in Information Systems

1. Weather forecaster

Tim lives in a rainy New England city. Outside of his window, Tim can see the town’s “Weather Forecaster” which is a set of lights atop the old tower.

This device works according to the following set of rules:

Light / Day
1 / Solid blue / Sunny
2 / Flashing blue / Cloudy
3 / Solid red / Rainy
4 / Flashing red / Snowy

Tim is only concerned with the rain. On any given morning, if Tim does not look at the “Weather forecaster”, Tim believes that there is 60% chance of rain.

Based on 4 years of experience, Tim assesses the following probabilities:

P(solid red |It will rain)=0.1

P(Flashing red | It will rain)=0.1

P(Solid blue | It will rain)=0.7

P(Flashing blue | It will rain)=0.1

P(solid red | It will not rain)=0.7

P(Flashing red | It will not rain)=0.1

P(Solid blue | It will not rain)=0.1

P(Flashing blue | It will not rain)=0.1

(a) When he gets up one Friday morning, Tim sees that the “Weather Forecaster” declares “Solid blue”. What is Tim’s chance that it will rain that day? Is Friday’s weather forecaster useful?

(b) The next morning Tim sees that the light is flashing, but can not tell the color because of a heavy fog. Now what is the probability that it will rain that day? Is Saturday’s weather forecaster useful?

2. The Taxicab problem

In Beer-Sheva there are two taxicab companies, the “blue” and the “green”. The "blue" company operates 90% of all cabs in the city and the "green" company the rest.

One dark evening John was involved in an accident. The only witness, David, says the cab was "green". In court it is noted that David might have a tendency to color blindness, and so the court ordered that David is to be tested under conditions similar to those in which the accident occurred.

In the test, when David is shown a "green" cab, he says it is "green" 80% of the time and "blue" 20% of the time. When David is shown a "blue" cab, he says it is "blue" 80% of the time and "green" 20% of the time. As a juror, you believe the test accurately represents his performance at the time of the accident, so the probabilities you assign to events during the accident agree with the frequencies the test reported.

(a) Draw the tree representing (first) the actual color of the cab and (second) David’s report of it. Label all endpoints, supply all branches probabilities, and calculate and label all endpoints probabilities.

(b) Flip (reverse) the tree. Label all branches, endpoints and probabilities.

(d) How does the answer to (c) compare to David’s accuracy on the test?

3. Preference Probability

The preference probability p of some prospect X when getting $200 and $20 are considered the best and worst outcomes respectively, is the one which makes you indifferent between getting X for sure of a chance p at $200 and a chance (1-p) at $20.

It is known that you follow the rules of actional thought (as introduced in the first lecture) and prefer more to less, and that your preference probabilities are as follows:

Dollars (X) / Preference Probability (p)
200 / 1.0
150 / 0.84
130 / 0.76
100 / 0.61
50 / 0.28
20 / 0.0

(a) Which of the rules of actional thought was mostly involved in determining your preference probabilities?

(b) Plot the preference probabilities in the range from 20$ to $200 with p on the vertical axis.

(d) What is your certain equivalent for the following deal?

4. Different People, Different U-curves

Daniel has the following u-curves:

x are total assets in dollars.

He owns $20 and the following lottery:

David has the u-curve , and he currently owns $75.

(a) What is Daniel’s certain equivalent for the lottery?

(b) How much money can you make buy buying Daniel’s lottery and selling it to David?

5. Risk Attitude

Bill has the following u-curve where x represents his total wealth in dollars.

(a) Plot Bill's u-curve.

(b) Bill owns exactly $10000. You offer to flip a coin, and if he calls it correctly, you will give him $3. However if Bill calls it incorrectly, he will pay $2. Should Bill accept this call?

(d) Characterize Bill's risk attitude in (b) and (c).

(e) What geometric feature of his u-curve corresponds to his risk attitude? Why?

(f) What risk attitude does a person with a logarithmic u-curve have?

6. Chewsy

Tri-National has recently developed Chewsy, a sugar-free gum that contains fluoride. Tri-National must decide whether or not to introduce Chewsy to the market. The sales of chewing gum are expected to total about $200 million over the next 10 years. Tri-National marketing staff feels that Chewsy could capture from 2 to 10 percent of the chewing gum market with front-end marketing campaign of $4 million. The marketing staff has assigned the following probabilities to the market share Tri-National could achieve:

Market Share Probabilities
High (10%) / 0.3
Medium (6%) / 0.5
Low (2%) / 0.2

Tri-National CFO points out that the profit margin on Chewsy is quite uncertain because of the unusual manufacturing requirements. He believes that there is a 40% chance that the profit margin will be only 25% of sales revenue and 60% chance it will be 50% of sales revenue. Tri-National is risk-neutral for deals of this size.

(a) Which alternative should Tri-National choose?

(b) Plot the cumulative distribution of profit for each alternative. What is the probability that your profits will exceed $4 million if Tri-National chooses to market Chewsy?

(c) What is the joint value of clairvoyance on both market share and profit margin? How does this compare with the sum of the value of clairvoyance on market share and the clairvoyance on profit margin?

(d) Plot your profit sensitivity to the probability of a high market share (assume that medium and low market remains at the same ratio). For what range of probabilities should Tri-National market Chewsy?

7. Mill's Dilemma

After exploring the Market Mr. Mill discovers the following ten years investment opportunity in Boesky Enterprises (BE):

(a) Assuming Mill is risk neutral, what is the value of his deal?

(b) Since Mill knows Ivan, head of BE, Mill can obtain perfect inside information on whether the stock will go up of down. What is the most Mill should pay for Ivan's inside information?

(c) Mill also has inside contacts in the Security & Exchange Commission (SEC). However, this information is not perfect. When the stock price goes up, the SEC says 90% of the time that it will go up; when the stock price goes down the SEC says 90% of the time that it will go down. What is the most Mill Should payfor the information from the SEC?

(d) Suppose that after obtaining the SEC information for $2.75 million, Mill believes that the stock will go up. Given this information, what is the most Mill should pay for Ivan's information?

8. Value of Information Without the D (delta) property

David is faced with a decision situation that is described by the tree below:

David's initial wealth is $50 and his u-curve is as follows, where x is his total wealth:

What is the value of clairvoyance on B to David? (Hint: For wealth states greater than 1, David does not subscribe to the delta property).

Recall that a decision maker who follows the delta property makes the same decisions whether he has a net worth increase by D before making the decision or the outcome of each possibility is increased by D.