1. Fundamentals of Decision Theory Models

2. Deciding Between Job Offers
Company A
In a new industry that could boom or bust.
Low starting salary, but could increase rapidly.
Located near friends, family and favorite sports team.
Company B
Established firm with financial strength and commitment to employees.
Higher starting salary but slower advancement opportunity.
Distant location, offering few cultural or sporting activities.
Which job would you take?

3. Good Decisions vs. Good Outcomes
A structured approach to decision making can help us make good decisions, but can’t guarantee good outcomes.
Good decisions sometimes result in bad outcomes.

4. Introduction
Decision theory is an analytical and systematic way to tackle problems A good decision is based on logic.

5. The Six Steps in Decision Theory
Clearly define the problem at hand
List the possible alternatives
Identify the possible outcomes & criteria
List the payoff or profit of each combination of alternatives and outcomes
Select one of the mathematical decision theory models
Apply the model and make your decision

6. Types of Decision-Making Environments
Type 1: Decision-making under certainty
decision-maker knows with certainty the consequences of every alternative or decision choice. (You know exact outcome; eg Savings Account)
Type 2: Decision-making under risk
decision-maker does know the probabilities of the various outcomes (You know the probability of each outcome; e.g. roll of die)
Type 3: Decision-making under uncertainty
decision-maker does not know the probabilities of the various outcomes (You know nothing, it is a wild guess at best)

7. Decision-Making Under Risk
Expected Monetary Value:
(Sum of the probabilities and outcome) n
nature, of
states
number
the to 1 j
where )
P(S *
Payoff i)
ative
EMV(Altern S = å

8. Example
You recently inherited $1,000 and are considering investing it in varied financial instruments. After Analyzing the economy (possibility of it being good or poor ) and the returns you can make in these conditions, you develop the following payoff table…

9. Decision Table
State Of Nature
Decision Alternative
Good Economy
Poor Economy
Portfolio 1 (high risk) 80
-20
Portfolio 2 (med risk) 30 20
Portfolio 3 (low risk) 23
Probability
0.3
0.7
Which portfolio should you invest in, that will maximize your returns?

10. Decision Table
State Of Nature
Decision Alternative
Good Economy
Poor Economy
EMV
Portfolio 1 (high risk) 80
-20 10
Portfolio 2 (med risk) 30 20 23
Portfolio 3 (low risk) 22
Probability
0.3
0.7
What is the maximum amount that should be paid for perfect forecast of the economy?

11. Expected Value of Perfect Information (EVPI)
EVPI places an upper bound on what one would pay for additional information EVPI is the expected value with perfect information minus the maximum EMV
EVPI = EV|PI - maximum EMV

12. EVPI = Expected Value with Perfect Information - max(EMV) =
State Of Nature
Decision Alternative
Good Economy
Poor Economy
EMV
Portfolio 1 (high risk) 80
-20
Portfolio 2 (med risk) 30 20 23
Portfolio 3 (low risk) 22
Probability
0.3
0.7
EVPI = Expected Value with Perfect Information - max(EMV) =
[80   0.7] – 23 = $16.4

13. Expected Opportunity Loss
EOL is the cost of not picking the best solution
EOL = Expected Regret
Work it the same way as EMV but just use the regret instead of payoffs.

14. EOL Table State Of Nature Decision Alternative Good Economy
Poor Economy
EOL
Portfolio 1 (high risk)
80 – 80 = 0
22 – (-20) = 42
Portfolio 2 (med risk)
80 – 30 = 50
22 – 20 = 2
Portfolio 3 (low risk)
80 – 22 = 58
22 – 22 = 0
Probability
0.3
0.7

15. EOL Table State Of Nature Decision Alternative Good Economy
Poor Economy
EOL
Portfolio 1 (high risk) 42
29.4
Portfolio 2 (med risk) 50 2
16.4
Portfolio 3 (low risk) 58
17.4
Probability
0.3
0.7

16. Sensitivity Analysis EMV(high risk) = $80P + (-$20) (1-P)
EMV(med risk) = $30P + $20(1-P)
EMV(low risk) = $22P + $22(1-P)

17. Sensitivity Analysis - continued
0.444
0.2
EMV (Med Risk)
EMV(low Risk)
EMV(High Risk)

18. Decision Making Under Uncertainty
Maximax
Maximin
Equally likely (Laplace)
Criterion of Realism
Minimax Regret

19. Decision Making Under Uncertainty
Maximax - Choose the alternative with the maximum output
States of Nature
Favorable Mkt ($)
Unfavorable Mkt ($)
Maximax
Construct Large Plant
200,000
-180,000
Construct Small Plant
100,000
-20,000
Do Nothing

20. Decision Making Under Uncertainty
Maximin - Choose the alternative with the maximum minimum output
States of Nature
Favorable Mkt ($)
Unfavorable Mkt ($)
Maximin
Construct Large Plant
200,000
-180,000
-18,000
Construct Small Plant
100,000
-20,000
Do Nothing

21. Decision Making Under Uncertainty
Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV
States of Nature
Favorable Mkt ($)
Unfavorable Mkt ($)
Equally Likely
Construct Large Plant
200,000
-180,000
10,000
Construct Small Plant
100,000
-20,000
40,000
Do Nothing
Probabilities
0.5

22. Decision Making Under Uncertainty
Criterion of Realism (Hurwicz): CR = *(row max) + (1-)*(row min)
=0.8
States of Nature
Favorable Mkt ($)
Unfavorable Mkt ($) CR
Construct Large Plant
200,000
-180,000
124,000
Construct Small Plant
100,000
-20,000
76,000
Do Nothing

23. Decision Making Under Uncertainty
Minimax - choose the alternative with the minimum maximum Opportunity Loss - this is using EOL table
States of Nature
Favorable Mkt ($)
Unfavorable Mkt ($)
Minimax Regret
Construct Large Plant
180,000
Construct Small Plant
100,000
20,000
Do Nothing
200,000
Probabilities
0.5

24. Summary Decision theory Decision Making under Risk
Decision Making under Uncertainty