Lecture Seven

1
Solving Influence Diagrams (Plus more Decision
Trees)
Reference Clemen Reilly. Making Hard
Decisions, Chapter 4.
NOTE Some materials for this presentation
courtesy of Dr. Dan Maxwell
2
Solving Trees for Expected Payoffs
Win
24
.20
(24 .2) (-1 .8) 4.80 - 0.80 4.00
Trade Ticket
Lose
-1
.80
Win
10
.45
Keep Ticket
(10 .45) (0 .55) 4.50 - 0 4.50
Lose
0
.55
4.00
Trade Ticket
We solve trees from right to left, reducing the
tree to the first decision node
Equivalent to
Keep Ticket
4.50
3
The Texaco - Pennzoil Case
In early 1984, Pennzoil and Getty Oil agreed to
the terms of a merger. But before any formal
documents could be signed, Texaco offered Getty
Oil a substantially better price, and Gordon
Getty, who controlled most of the Getty stock,
reneged on the Pennzoil deal and sold to Texaco.
Naturally, Pennzoil felt as if it had been dealt
with unfairly and immediately filed a lawsuit
against Texaco alleging that Texaco had
interfered illegally in the Pennzoil-Getty
negotiations. Pennzoil won the case in late
1985, it was awarded 11.1 billion, the largest
judgment ever in the United States. A Texas
appeals court reduced the judgment by 2 billion,
but interest and penalties drove the total back
up to 10.3 billion. James Kinnear, Texaco's
chief executive officer, had said that Texaco
would file for bankruptcy if Pennzoil obtained
court permission to secure the judgment by filing
liens against Texaco's assets. Furthermore,
Kinnear had promised to fight the case all the
way to the U.S. Supreme Court if necessary,
arguing in part that Pennzoil had not followed
Security and Exchange Commission regulations in
its negotiations with Getty. In April 1987, just
before Pennzoil began to file the liens, Texaco
offered to pay Pennzoil 2 billion to settle the
entire case. Hugh Liedtke, chairman of Pennzoil,
indicated that his advisors were telling him that
a settlement of between 3 billion and 5 billion
would be fair.
4
Pennzoil Decision Tree
Solve right to left
5
Pennzoil Decision Tree
Expected Values
2 B
5 B
4.63 B
4.56 B
4.63 B
4.56 B
4.56 B
3 B
Expected Payoff 4.63 Billion
6
Pennzoil Influence Diagram
7
How the Influence DiagramThinks About the Case
8
Side by Side
Side-by-side First Pennzoil Decision
This is tree for Pennzoil first Decision,
representing Texaco Chance Node as Tree Branches
9
Payoff Table (1)
It doesnt matter what is inside this box if you
have already accepted 2 Billion
10
Payoff Table (2)
Refuse 2B, 5B, 3B
Go with Court Order
Refused both 2 B and 5 B
11
First Step in Solving
Texaco Reaction
Accept 2 Billion?
Revised Payoff Table (Using Expected Values for
Court Decision)
Final Court Decision
Pennzoil Reaction
12
Second Step in Solving
Texaco Reaction
Accept 2 Billion?
Final Court Decision
13
Final Step in Solving
Texaco Reaction
Accept 2 Billion?
Final Court Decision
Accept Expected Payoff 2 Billion? (
Billion) Accept 2 2.0 Offer 5
4.63
14
Influence Diagram Algorithm

• Clean up the influence diagram
• Only one consequence (payoff) node
• No cycles
• No barren nodes
• Check for Chance Nodes in wrong place
• Directly before consequence node
• Not directly before any other node
• Turn these into expected value nodes
• Look for certain Decision Nodes
• Directly before consequence node
• Its predecessors are same as all direct
  predecessors of consequence node
• Reduce to the optimum value

15
Solving Influence Diagrams

• Influence Diagrams are usually solved using
  software
• Freeware and Commercial software exists
• For exam, follow procedure used in todays
  lecture
• Read Chapter 4 pages 111-125