Decision Theory Homework 1) The payoff table showing profit for a decision analysis problem with two decisions and three states of nature is shown below. a. Solve this problem using a payoff matrix b. Construct a decision tree for this problem. c. Evaluate the decision tree. 2) Suppose a decision maker is faced with four decisions alternatives and four states of nature as shown in the table below. a. Solve this problem using a payoff matrix b. Construct a decision tree for this problem. c. Evaluate the decision tree. ) You are a betting person and wish to bet on the State University varsity/alumni game. (In other words you have a gambling addiction and you are going to bet. ) You have no information on the odds for either team’s winning. The only information you have is that the varsity has won 12 and the alumni have won 8. Ties are broken by sudden death playoffs. You have an opportunity to do some research into the strengths and weaknesses of the two teams; the outcome of this research will predict a winner. The only bet you can make is an even $100. I1 = research indicates varsity will win.

I2 = research indicates the alumni will win. S1 = varsity will win. S2 = alumni will win. P(I1|S1) = . 70 P(I2|S1) = . 30 P(I1|S2) = . 40 P(I2|S2) = . 60 a. Draw the decision tree and label it. b. Evaluate the tree c. What is your strategy and EMV? d. What is the most that you would be willing to pay for someone to do the research for you? e. Assuming that the games are fixed. How much would you be willing to pay the person who fixes the games to tell you which team is going to win? 4) An oil company must decide whether or not to drill an oil well in a particular area.

The decision maker believes that the area could be dry, reasonably good, or a bonanza, with the respective probabilities of . 40, . 40, and . 20. If the well is dry, no revenue is generated. If the well is reasonably good, the expected revenue is $75,000. If the well is a bonanza, the expected revenue is $200,000. In any case, the cost of drilling the well is $40,000. At a cost of $15,000, the company can take a series of seismic soundings determining the underlying geological structure at the site. These experiments will disclose whether there is no structure, open structure, or closed structure.

Let us denote these experimental outcomes as I1, I2, and I3 respectively. Let S1 = dry hole S2 = reasonably good potential S3 = bonanza Past experience has indicated the following conditional probabilities: P(I1|S1) = . 60P(I1|S2) = . 40P(I1|S3) = . 10 P(I2|S1) = . 30P(I2|S2) = . 40P(I2|S3) = . 40 P(I3|S1) = . 10P(I3|S2) = . 20P(I3|S3) = . 50 a. Draw and label the decision tree for this problem. b. Evaluate the decision tree. c. What is the optimal strategy? d. What is the EMV of the optimal strategy? e. Should you be willing to pay $15,000 for the soundings? f. What is the EVPI?