Company Case

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3 12 B (.7) 12 + (.3)3 = 9.3

-2 15 ** S (.7) 15 + (.3)-2 = 9.9 **

6.5 ** 6.5 D (.7) 6.5 + (.3)6.5 = 6.5

Best Worst

4. Minimizing Regret

5. Equal Likely Strategy (LaPlace)

Opportunity Loss Matrix Action

Action Growth No Change Inflation Max/Row Bonds** 7 **

Bonds -3 (12-15) -0.5 -3.5 -3.5 ** Stocks 5.3

Stocks 0 -3.5 -8.5 -8.5 Deposit 6.5

Dep. -8.5 0 0 -8.5

DECISION MAKING UNDER RISK

1. Expected Payoff (Average) 2. Expected Opportunity Loss

Opportunity Loss (EOL) Matrix

Action Average Payoff _ Act G (.5) No (.3) In (.2) EOL

** Bonds (.5)12 + (.3)6 + (.2)3 = 8.4 **

B** 3 (15-12) 0.5 3.5 2.35**

Stocks (.5)15 + (.3)3 + (.2)-2 = 8.0

S 0 3.5 8.5 2.75

Deposit (.5)6.5 + (.3)6.5 + (.2)(6.5)= 6.5

D 8.5 0 0 4.25

3. Most Probable State of Nature

Action Growth (.5) Note: EOL is the sum of the (prob.* loss)

Bounds 12 3(.5) + .5(.3) + 3.5(.2) = 2.35

Stocks 15** 0(.5) + 3.5(.3) + 9.5(.2) = 2.75

Deposit 6.5 8.5(.5) + 0(3) + 0(.2) = 4.25

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4. Expected Value of Perfect Information

EVPI = ERPI - Average Expected Payoff

Max Values from Each Column

Growth(.5) No Change(.3) Inflation(.2)

15 6.5 6.5

ERPI= 15(.5) + 6.5(.3) + 6.5(.2) = 10.75

EVPI = 10.75 - 8.4 = 2.35%

If information costs more than 2.35%, don't buy it. If you invest $100.000 should you buy info for $15,000? 2.35% ($100,000) - $15,000 = -$12,650 => NO!

DECISION TREES (Bayesian Approach)

1. Evaluate the Decision with Prior Probabilities

State of Nature

Action A (High Sales) (.2) B (Medium Sales) (.5) C (No Sales) (.3)

A1 (Develop) 3000 2000 -6000

A2 (Don't) 0 0 0

Prior EMV : Develop: (.2)3000 + (.5)2000 + (.3)(-6000) = -200

Prior EMV (Don't): 0 **

2. Acquire Some Reliable Info (Not Perfect Info Due To Uncertainty)

GIVEN

Predicted A (High) B (Medium) C (Small)

Ap 0.8 0.1 0.1

Bp 0.1 0.9 0.2 Consultant is best at

Cp 0.1 0.0 0.7 Predicting medium sales.

Sum 1.0 1.0 1.0

3. Revised (Posterior) Probabilities are Computed

Predictions

State of Nature |Ap Bp Cp | Prior Prob. | Ap . P | Bp . P | Cp . P |

A | .8 .1 .1 | .2 | .16 | .02 | .02

B | .1 .9 0 | .5 | .05 | .45 | 0

C | .1 .2 .7 | .3 | .03 | .06 | .21

Sum | .24 | .53 | .23 _ add-up to 1

0.2= P(Bp|C) |.16/.24| .02/.53| .02/.23

Note: Table is inverted, now |= .667 | = .038 | = .087

rows add to equal 1. |.05/.24| .45/.53| 0/.23

See decision tree for use of values |= .208 | = .849 | = 0

|.03/.24| .06/.53 | .21/.23

0.113=P(C|Bp) |= .125 | = .113 | = .913

Sum 1 1 1

4. Expected Values Are Computed: See decision tree

5. A decision is made regarding whether or not to acquire the additional info. Then a choice is made immediately.

6. If a decision is made to buy the info, then the research is undertaken only after that,