Question

The following is a payoff table giving profits for various situations.

States of Nature Alternatives A B C D

Alternative 1 120 140 170 160

Alternative 2 210 130 140 120

Alternative 3 120 140 110 190

Do Nothing 0 0 0 0

a. What decision would a pessimist make?

b. What decision would an optimist make?

c. What decision would be made based on the realism criterion, where the coefficient of realism is 0.60?

d. What decision would be made based on the equally likely criterion?

e. What decision would be made based on the minimax regret criterion? Suppose now that the probabilities of the 4 states of nature are known, that is, the probability to observe A is 30%, the probability to observe B is 35%, the probability to observe C is 20%, and the probability to observe D is 15%. Answer the following

f. What decision would be made based on the expected monetary value?

g. What is the EVPI

Answer 1

a) A pessimist would make a decision based on the maximin payoff ie the maximum of the minimum payoffs that he would receive under the 4 different alternatives.

The minimum payoffs are 120,120,110,0

So we can see that the maximum of the minimum are 120 under alternative 1 &2 however if we look at the next payoff which is just above 120 for both the alternatives it's 140 for alternative 1 and 130 for alternative 2. So Alternative 1 is better than alternative 2 under the maximin criteria

Hence the pessimist would choose alternative 1.

b. Optimist would go for the maximax criteria ie the best payoff.

The max payoffs under each criteria are 170,210,190,0

So the maximum of the maximum payoffs is 210 under Alternative 3, so the optimist would choose this alternative.

c. Realism criteria = maximum return*realism coefficient + minimum return*(1-realism coefficient)

So for Alternative 1: 170*0.6 + 120*0.4 = 150

Alternative 2: 210*0.6 + 120*0.4 = 174

Alternative 3: 190*0.6 + 110*0.4 = 158

Alternative 4 =0

So we can see that payoff under realism criteria is maximized under Alternative 2 hence this is the best alternative here.

d. Equally likely criteria = the criteria where we assume that each state of nature occurs with the same probability. So the probability here is 1/4. We multiply the probability with the payoffs.

Alternative 1: 120*1/4 + 140*1/4 + 170*1/4 + 160*1/4 = 147.5

Alternative 2: (210+130+140+120)/4 = 150

Alternative 3: (120+140+110+190)/4 = 140

Alternative 4: 0

Again we see that the payoff is maximized under alternative 2, so it's the best decision here.