4: CHAPTER MAKING CHOICES OVERVIEW determining the preferred alternative - decision trees - influence diagrams risk profiles dominance considerations decision analysis software CASE STUDY: TEXACO VERSUS PENNZOIL problem description, pp. 101-105. draw the decision tree - what are the values? - what are the decisions? - what are the uncertainties? - what is the sequence?
decision tree constructed with DPL
Hugh Liedtke's Decision
Texaco Reaction Accept $2B Accept $2B 2 Counteroffer $5B Texaco Accepts $5B 0.17 5 Texaco Refuses Counter 0.5
Final Court Decision
0.2 a Pennzoil Reaction Refuse Texaco Counters $3B 0.33 0.5 0.3 a
10.3 5 0
Accept $3B 3
QUESTIONS 1. Does the decision tree capture the fundamental structure of Liedtke's decision? 2. What are some of the simplifying assumptions made in the decision tree? 3. Is the tree symmetric or asymmetric? PROBABILITIES based on DM's state of information obtained from data and individuals that the DM trusts
two uncertain events - Texaco's response (DM & advisors) 0.5 chance Texaco refuses to negotiate if Texaco negotiates, 2/3 chance counteroffer $3B - final court decision (DM & advisors) 0.2 chance court awards $10.3B 0.3 chance court awards $0B DECISION TREES AND EXPECTED MONETARY VALUE decision criteria: highest expected monetary value (EMV) to determine the best decision "now" we must consider the best "future" decisions solution procedure: average out and fold back - work backwards from outcomes to the first decision apply the solution procedure to the decision tree QUESTIONS 1. If we maximize EMV, what is the optimal strategy? 2. If Liedtke decides to counteroffer $5B and Texaco counteroffers $3.5B, what should Liedtke do? 3. Has the state of information changed?
SOLVE THE DECISION TREE WITH DPL
Accept__2B
[2] 2 Texaco_Accepts__5B .170 [5] 5 s1 Final_Court_Decision Texaco_Refuses_Counter [4.56] .200 s2 .500 s3 .300 [10.3] 10.3 [5] 5 [0] 0 s1 Pennzoil_Reaction Texaco_Counters__3B [4.56] .330 Accept__3B [3] 3 Refuse Final_Court_Decision [4.56] .200 s2 .500 s3 .300 [10.3] 10.3 [5] 5 [0] 0
Accept__2B [4.6348]
.500 Texaco_Reaction Counteroffer__5B [4.6348]
THE DPL WAY: USES ADVANTAGES OF ID AND DT draw an ID for the Texaco-Pennzoil case
ID & DT TO SOLVE: Using get-pays
Texaco Reaction Accept $2B All arrows are black Payoff Pennzoil Reaction
We put all the key data (outcomes, decision alternatives, probabilities and
Final Court Decision
Accept__2B
Accept $2B 2 Counter $ 5B 0
consequence) in the ID nodes
Accept $5B 0.17 Refuse 0.5 Counter $3B 0.33
Texaco_Reaction
5 0 0
Pennzoil_Reaction
Refuse 0 Accept $3B 3
QUESTION: Why have we put value data in the two decision nodes?
Final_Court_Decision
High 0.2 Medium 0.5 Low 0.3
10.3 5 0
Next, we tab to the DT mode. DPL builds a symmetric tree.
Texaco's Reaction Accept $2B? Accept $5B Accept $2B Refuse Offer $5B Counter $3B
Pennzoil Reaction Accept $3B Refuse
Final Court Decison
N10.3 B Payoff N5.0 B Payoff N0 Payoff
Sometimes we have to reorder the nodes if they are not in the correct sequence. Next, we have to structure the decision tree to correctly order the decision and
the chance nodes
Texaco Reaction Accept $5B Texaco_Reaction Refuse
Accept $2B Accept $2B Accept__2B Counter $ 5B
Final Court Decision
High Final_Court_Decision Medium Final_Court_Decision Low Final_Court_Decision Pennzoil Reaction Refuse
a
Counter $3B
a
Accept $3B Pennzoil_Reaction
NOTES: 1. I had to delete and add back in three of the nodes, one outcome at a time. Which three? 2. What does tha "a" node mean? 3. I have added the variable names for the branch "Get/Pays" in the DT mode. Where does DPL get the data for these variables? 4. Every path through the decision tree must have the correct "Get/Pays."
Here's the DPL solution.
Accept__2B
[2] 2 Accept__5B .170 [5] 5 High [10.3] 10.3 [5] 5 [0] .200 Medium .500 Low .300 Pennzoil_Reaction Counter__3B [4.56] .330
Accept__2B [4.6348]
Texaco_Reaction Counter___5B [4.6348]
Final_Court_Decision Refuse [4.56] .500
0 Final_Court_Decision Refuse [4.56] Accept__3B [3] 3
QUESTIONS: 1. How does it differ from the first decision tree solution? 2. Which of the approaches seems the easiest for this problem? STRONG RECOMMENDATIONS: 1. Work you way through the DPL ID and DT tutorials. 2. Try to duplicate DT and ID/DT approaches and see if you can get the correct answer. 3. If you can not do the tutorials or the DPL work in the notes: SEE ME FOR HELP! SOLVING INFLUENCE DIAGRAMS
A very simple discussion on the ID solution algorithm is given in the text in an optional section. The ID algorithm was developed by Shachter, 1986 The algorithm operates by node reduction We won't cover it in class. BOTTOM LINE: DT and ID algorithm give the same solution. RISK PROFILES EMV is not expected and, in most cases, is not even feasible!!! we examine risk by looking at the risk profiles (probability mass functions) of the alternative decisions
QUESTIONS: 1. What is the risk profile of the Accept $2B alternative?
2. What is the risk profile of the optimal decision strategy?
Here is the DPL risk profile plots
Risk Profiles (Format, Common Y scale)
1 0.9
0.8
0.7
Accept__ 2B_:
0.6
Accept__2B
0.5
Accept__ 2B_:
0.4
Offer__5B
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
QUESTIONS: 1. What is the x-axis?
2. What is the y-axis? CUMULATIVE RISK PROFILES Draw the cumulative risk profile (the cumulative distribution for each of the two initial decisions
Here's the DPL cumulative distributions
CUMMULATIVE RISK PROFILES
1 0.9 0.8
0.7
Accept__2B:
0.6
Accept__2B
0.5
Accept__2B:
0.4
Counter___5B
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
QUESTIONS 1. How do we get the to probabilities plot the Risk Profile? 2. How do we plot the Cumulative Risk Profile? 3. Are the Risk Profiles and Cumulative Risk Profiles equivalent? 4. Which one is easier to explain to senior decision-makers? 5. Suppose the worst possible outcome in the Final Court Decision was $2.5B instead of $0B, how would that change the Risk Profile and the Cumulative Risk Profile? I'm going to use the ID/DT approach. I only need to change the consequences of one outcome in the Final Court Decision chance node
High Final_Court_Decision 0.2 Medium 0.5 Low 0.3 10.3 5 2.5
Here's the DPL solution
Accept__2B
[2] 2 Accept__5B .170 [5] 5 High [10.3] 10.3 [5] 5 [2.5] 2.5 Final_Court_Decision [5.31] [3] 3 Final_Court_Decision [5.31] .200 Medium .500 Low .300 Pennzoil_Reaction Counter__3B [5.31] .330 Refuse
Accept__2B [5.2573]
Texaco_Reaction Counter___5B [5.2573]
Refuse .500
Accept__3B
Here's the cumulative risk profiles
Cummulative Risk Profiles
1 0.9 0.8
0.7
A c cept__2B:
0.6
Ac c ept__2B
0.5
A c cept__2B:
0.4
Counter___5B
0.3
0.2
0.1
0
2
3
4
5
6
7
8
9
10
6. Explain this chart in terms a senior manager would understand ALTERNATIVES THAT DOMINATE deterministic dominance: the dominating alternative is always at least as good as the dominated alternative - see previous problem Suppose Firm A charges less if it goes to court than Firm B. - probabilities are the same
stochastic (probabilistic) dominance: in a cumulative risk profile, an alternative stochastically dominates if it is always lower and to the right of all other alternatives
Suppose we have two law firms that charge a different amount. I now modify the decision tree as follows
ID & DT TO SOLVE: Using get-pays
Blue Select Law Firm Final Court Decision
Texaco Reaction
All arrows are black Payoff
Accept $2B Pennzoil Reaction
What does the blue arrow mean?
High Final_Court_Decision A Medium 5.2 Low 0 High Final_Court_Decision B Medium 5 Low 0 10.3 10.5
elect_Law_Firm
I had to add the new decision node to the DT
Texaco Reaction Accept $5B Texaco_Reaction Refuse
Accept $2B Select Law Firm A a Accept $2B Accept__2B Counter $ 5B
Final Court Decision
High b Final_Court_Decision Medium Final_Court_Decision Low Final_Court_Decision
B
a
Pennzoil Reaction Refuse Counter $3B Accept $3B
b
Pennzoil_Reaction
The DPL solution is
Accept__2B
[2] 2 Accept__5B .170 [5] 5 High [10.5] 10.5 [5.2] 5.2 [0] 0 .200 Medium .500 Low .300 Pennzoil_Reaction Counter__3B [4.7] .330
Select_Law_Firm [4.751]
A
Accept__2B [4.751]
Texaco_Reaction Counter___5B [4.751]
Final_Court_Decision Refuse [4.7] .500
Final_Court_Decision Refuse [4.7] Accept__3B [3] 3
B
Accept__2B [4.6348]
the cumulative risk profile is
1
Cummulative Risk Profile
0. 9
0. 8
0. 7
Select_Law_F irm :
0. 6
A
0. 5
Select_Law_F irm :
0. 4
B
0. 3
0. 2
0. 1
0
0
1
2
3
4
5
6
7
8
9
10
11
QUESTIONS: 1. Do we have deterministic dominance? 2. Do we have stochastic dominance? suppose we change the probabilities instead of the outcomes
QUESTIONS: 1. How do I change the ID? 2. How do I change the DT?
the new ID is
ID & DT TO SOLVE: Using get-pays
Green Select Law Firm Final Court Decision
Texaco Reaction
All arrows are black Payoff
Accept $2B Pennzoil Reaction
What does the green arrow mean?
High Final_Court_Decision A Select_Law_Firm 0.3 Medium 0.6 Low High Final_Court_Decision B 0.2 Medium 0.5 Low
Note that you do not have to put in the last probability
High Final_Court_Decision Medium 5 Low 0 10.3
the DPL solution is
Accept__2B
[2] 2 Accept__5B .170 [5] 5 High .300 Medium .600 Low .100 Refuse [10.3] 10.3 [5] 5 [0] 0 Final_Court_Decision [6.09] [3] 3
Select_Law_Firm [5.9047]
A
Accept__2B [5.9047] Counter___5B
Texaco_Reaction [5.9047]
Refuse .500
Final_Court_Decision [6.09]
Counter__3B .330 B Accept__2B [4.6348]
Pennzoil_Reaction [6.09]
Accept__3B
QUESTIONS: What do you expect the cumulative risk profiles to show? the resulting cumulative risk profile
Cummulative Risk Profiles
1 0 .9 0 .8
0 .7
Se lec t_ L aw _ Firm :
0 .6
A
0 .5
Se lec t_ L aw _ Firm :
0 .4
B
0 .3
0 .2
0 .1
0
0
1
2
3
4
5
6
7
8
9
10
QUESTIONS: 1. Do we have deterministic dominance? 2. Do we have stochastic dominance? stochastic dominance results from higher payoffs and/or higher probabilities MOTIVATION: screening alternatives saves analysis time QUESTIONS: 1. Will an alternative that deterministically dominates have a higher EMV? 2. Will the alternative that stochastically dominates have a higher EMV? ADVICE: ALWAYS CHECK FOR DOMINANCE FIRST!! DPL POLICY SUMMARY:
Most useful DPL tools to understand the solution (or debug a DA model) Obtain from DPL Decision Policy screen, use View (Policy Summary) or Control-S
Accept__2B
Pennzoil_Reaction
Accept__2B 0 Counter___5B 1 (does not occur) 0
Refuse 0.33 Accept__3B 0 (does not occur) 0.67
Texaco_Reaction
Accept__5B 0.17 Refuse 0.5 Counter__3B 0.33 (does not occur) 0
Final_Court_Decision
High 0.166 Medium 0.415 Low 0.249 (does not occur) 0.17
QUESTIONS: 1. How do we read the policy summary? 2. How can it be used to interpret the optimal strategy? 3. How can it be used to debug or validate a decision model? BOTTOMLINE: The policy summary is very useful when there are a large number of variables! In such cases, printing out and interpreting the DT is difficult. DECISION ANALYSIS SOFTWARE
Buede, Dennis, "Aiding Insight III," OR/MS, Volume 23, No. 4, August 1996, pp. 73-79 [3rd decision analysis software survey] Copies of Data available for student use. SUMMARY determining the preferred alternative - decision trees - influence diagrams risk profiles - Risk Profile & Cumulative Risk Profile dominance considerations decision analysis software