Question 5.p.3: Using the information in the payoff table, develop a table o...
Using the information in the payoff table, develop a table of regrets, and then:
a. Determine the alternative that would be chosen under minimax regret.
b. Determine the expected value of perfect information using the regret table, assuming that the probability of a new bridge being built is .60.
To obtain the regrets, subtract all payoffs in each column from the best payoff in the column. The regrets are
| New Bridge |
No New Bridge |
|
| A | 3 | 0 |
| B | 2 | 4 |
| C | 0 | 8 |
a. Minimax regret involves finding the worst regret for each alternative and then choosing the alternative that has the “best” worst. Thus, you would choose A:
| Worst | |
| A | 3[best] |
| B | 4 |
| C | 8 |
b. Once the regret table has been developed, you can compute the EVPI as the smallest expected regret. Because the probability of a new bridge is given as .60, we can deduce that the probability of no new bridge is 1.00 – .60 = .40. The expected regrets are
A: .60(3) + .40(0) = 1.80
B: .60(2) + .40(4) = 2.80
C: .60(0) + .40(8) = 3.20
Hence, the EVPI is 1.80.