# Decision Making Models

Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following payoff table:

Decision State of Nature

Alternatives S1 S2 S3 S4

D1 909 1117 952 307

D2 252 457 505 1088

D3 1108 643 1075 841

D4 1120 558 629 1178

a) What alternative would you recommend to an optimistic decision-maker? What is the expected payoff of this decision?

b) What alternative would you recommend to an pessimistic decision-maker? What is the expected payoff of this decision?

c) What alternative would you recommend using the equal-likelihood criterion? What is the expected payoff of this decision?

d) What alternative would you recommend using the minimax regret criterion? What is the expected payoff of this decision?

https://brainmass.com/statistics/central-tendency/decision-making-models-466807

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please refer attached file for better clarity of tables.

a)

A optimistic decision maker will use the Maximax decision rule to make a decision.

State of Nature Maximum

Decision Alternative S1 S2 S3 S4 Payoff

D1 909 1117 952 307 1117

D2 252 457 505 1088 1088

D3 1108 643 1075 841 1108

D4 1120 558 629 1178 1178

Maximum of maximum payoffs is $1178. He should choose D4. Expected payoff is 1178.

b)

A pessimistic decision maker will use the Maximin decision rule to make a decision.

The maximin criterion suggests that the decision-maker should

choose the alternative which maximizes the minimum payoff he can get.

State of Nature Minimum

Decision Alternative S1 S2 S3 S4 Payoff

D1 909 1117 952 307 307

D2 252 457 505 1088 252

D3 1108 643 1075 841 643

D4 1120 558 629 1178 558

Maximum payoff from minimum Payoffs is $643. He should choose D3. Expected Payoff is $643.

c)

In equally likelihood criterion, decision maker will assign equal probability for each of the state of nature.

Then he will choose the alternative with highest expected value.

There are 4 states of nature possible in this case. So,

Probability of each state=1/4=0.25

State of Nature

Decision Alternative S1 S2 S3 S4

Probability-----> 0.25 0.25 0.25 0.25

D1 909 1117 952 307

D2 252 457 505 1088

D3 1108 643 1075 841

D4 1120 558 629 1178

Expected Payoff For D1=0.25*909+0.25*1117+0.25*952+0.25*307=821.25

Expected Payoff For D2=0.25*252+0.25*457+0.25*505+0.25*1088=575.50

Expected Payoff For D3=0.25*1108+0.25*643+0.25*1075+0.25*841=916.75

Expected Payoff For D4=0.25*1120+0.25*558+0.25*629+0.25*1178=871.25

Highest expected payoff is $916.75. He should choose D3. Expected Payoff is $916.75

d)

First we find highest payoff in each state of nature.

State of Nature

Decision Alternative S1 S2 S3 S4

D1 909 1117 952 307

D2 252 457 505 1088

D3 1108 643 1075 841

D4 1120 558 629 1178

Column max 1120 1117 1075 1178

Now we will make regret table.

Regret Table

State of Nature Maximum

Decision Alternative S1 S2 S3 S4 Regret

D1 211 0 123 871 871

D2 868 660 570 90 868

D3 12 474 0 337 474

D4 0 559 446 0 559

Minimum of maximum regret is $474. Decision should be D3.

Expected Payoff is $643.

https://brainmass.com/statistics/central-tendency/decision-making-models-466807