Decision Making Analysis About Penzoil

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  • Topic: Decision theory, Decision tree, Influence diagram
  • Pages : 10 (865 words )
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  • Published : March 13, 2013
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Making Choices

동국대학교 산업시스템공학과 의사결정연구실

Case: Texaco vs. Penzoil


Hue Liedtke’s decision tree
Accept $2 Billion Texaco Accepts $5 Billion (0.17)
(0.2) Settlement Amount ($ Billion) 2 5 10.3 5 0 10.3 5 0 3

Counteroffer $5 Billion

Texaco Refuses Counteroffer (0.50)

Final Court Decision

(0.5) (0.3)

Texaco Counteroffers $3 Billion (0.33)

(0.2) Refuse Final Court Decision (0.5) (0.3) Accept $3 Billion

Decision Tree and EMV




Expected Value (EV) Expected Monetary Value (EMV) Folding back the tree (Averaging-out and folding-back process) 





Start at the end-points of the branches on the far right-hand side and move to the left Calculate expected value when you encounter a chance node Choose the branch with the highest value or expected value when you encounter a decision node

Case: Texaco vs. Penzoil


Hue Liedtke’s solved decision tree
Accept $2 Billion
Settlement Amount ($ Billion) 2

4.63

Texaco Accepts $5 Billion (0.17)
(0.2)

5 10.3 5 0 10.3 5 0 3

Counteroffer $5 Billion

4.63
Texaco Refuses Counteroffer (0.50)

4.56
Final Court Decision (0.5) (0.3) (0.2)

Texaco Counteroffers $3 Billion (0.33)

4.56
Refuse Final Court Decision (0.5) (0.3) Accept $3 Billion

4.56

Case: Texaco vs. Penzoil


Influence diagram for Liedtke’s decision
Accept $2 Billion?
Alternatives Accept 2 Counter 5

Texaco Reaction
Outcomes (Prob) Accept 5 (0.17) Refuse (0.50) Counter 3 (0.33)

Penzoil Reaction
Alternatives Accept 3 Refuse

Settlement Amount
Amounts: …

Final Court Decision
Outcomes (Prob) $10.3 Billion (0.2) $5.0 Billion (0.5) $0 (0.3)

Risk Profiles


A Risk profile: “a graph that shows the chances associated with possible consequences” Each risk profile is associated with a strategy. In constructing a risk profile, we collapse a decision tree by multiplying out the probabilities on sequential chance branches. At a decision node, only one branch is taken.



Case: Texaco vs. Penzoil


Risk profile for the “Accept $2 Billion” alternative
Chance that settlement equals x (%) 100 75 50 25 100%

0

2

4

6 x ($ Billion)

8

10

12

Case: Texaco vs. Penzoil


Risk profile for the “Counteroffer $5 Billion; Refuse Texaco Counteroffer” strategy Chance that settlement equals x (%) 100 75 58.5% 50 25 24.9% 16.6%

0

2

4

6 x ($ Billion)

8

10

12

Case: Texaco vs. Penzoil


Risk profile for the “Counteroffer $5 Billion; Accept $3 Billion” strategy Chance that settlement equals x (%) 100 75 50 33% 25 15%

42%

10% 2 4 6 x ($ Billion) 8 10 12

0

Case: Texaco vs. Penzoil


Cumulative risk profile for the “Counteroffer $5 Billion; Refuse Texaco Counteroffer” Chance that payment is less than or equal to x (%) 100 75 50 25

0

2

4

6 x ($ Billion)

8

10

12

Dominance: An Alternative to EMV


Using the idea of dominance, we can identify those profiles (and their associated strategies) that can be ignored. Such strategies are said to be dominated, because we can show logically, according to some rules relating to cumulative risk profiles, that there are better risks (strategies) available.



Types of dominance
 

Deterministic dominance Probabilistic dominance

Dominance: An Alternative to EMV
Deterministic dominance




The dominating alternative pays off at least as much as the one that is dominated. Settlement Example: Amount ($ Billion) Accept $2 Billion
2 Texaco Accepts $5 Billion (0.17) Counteroffer $5 Billion Texaco Refuses Counteroffer (0.50) Refuse Final Court Decision (0.2) (0.5) 5 (0.3) 2.5 10.3 Final Court Decision Accept $3 Billion (0.5) 5 (0.3) 2.5

5
10.3

Texaco Counteroffers $3 Billion (0.33)

(0.2)

3

Dominance: An Alternative to EMV
Deterministic dominance


Another Example:
예상 수익(100만원)
건조한 기후

40
고추를 심는다 보통 기후

50
습한 기후

30
건조한 기후

20
보통 기후

40
배추를 심는다 습한 기후

30...
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