Write out the payoff table for the investor€™s decision problem.

An Introduction to Decision Analysis, 2nd ed., Robert T. Clemen presents an example in which an investor wishes to choose between investing money in (1) a high-risk stock, (2) a low-risk stock, or (3) a savings account. The payoffs received from the two stocks will depend on the behavior of the stock market€”that is, whether the market goes up, stays the same, or goes down over the investment period. In addition, in order to obtain more information about the market behavior that might be anticipated during the investment period, the investor can hire an economist as a consultant who will predict the future market behavior. The results of the consultation will be one of the following three possibilities: (1) €œeconomist says up,€ (2) €œeconomist says flat€ (the same), or (3) €œeconomist says down.€ The conditional probabilities that express the ability of the economist to accurately forecast market behavior are given in the following table:

For instance, using this table we see that P(€œeconomist says up€ u market up) 5 .80. Figure 18.7 on the next page gives an incomplete decision tree for the investor€™s situation. Notice that this decision tree gives all relevant payoffs and also gives the prior probabilities of up, flat, and down, which are, respectively, 0.5, 0.3, and 0.2.

Figure 18.7

True Market State Flat Down Economist's Prediction "Economist says up" "Economist says flat" "Economist says down" Up .80 .15 .20 .10 .20 .60 .70 .15 .10 Market Activity Up (0.5) Flat (0.3) 1,500 100 Down (0.2) High-risk stock -1,000 Up (0.5) 1,000 Low-risk Flat (0.3) 200 Down (0.2) stock 100 Market Activity Savings account Up (?) Flat (?) 500 1,500 High-risk stock 100 Consult Down (?) economist -1,000 Up (?) 1,000 Low-risk stock Flat (?) Economist's 200 Down (?) Forecast - 100 Savings account 500 Economist says "market up" (?) Up (?) 1,500 High-risk stock Flat (?) 100 Down (?) -1,000 Up (?) 1,000 Economist says Low-risk stock Flat (?) 200 "market flat (?) Down (?) - 100 Savings account 500 Economist says Up (?) "market down" 1,500 (?) High-risk stock Flat (?) 100 Down (?) -1,000 Up (?) 1,000 Low-risk stock Flat (?) 200 Down (?) -100 Savings account 500