Solving Influence Diagrams

1
Solving Influence Diagrams

• Influence Diagrams are usually solved using
  software
• Freeware and Commercial software exists
• For the exam, follow procedure used in todays
  lecture

2
Simple tricks for Solving Influence Diagrams

• If you have a decision tree, the same squares
  and circles will appear as decision boxes and
  events respectively on the influence diagram
• If 2 circles (event with outcomes) are identical
  they appear only once on the influence diagram
  (compare slides 4 an 5 of the Pennzoil problem,
  court decision appears only once)
• In addition to the above measures appear on
  influence diagrams to add more meaning, examples
  include cost, debt, revenue
• Connect them using arrows to indicate influence
  and information flow relationships

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
Steps to draw Influence Diagram from a Decision
Tree

• Step 1
• Draw the squares for decision boxes, circles for
  events with outcomes and a payoff box

Texaco Reaction
Final Court Decision
Accept 2 Billion?
Pennzoil Reaction
6
Steps to draw Influence Diagram from a Decision
Tree

• Step 2
• Write the alternative (choices) for decision box,
  and outcome for events

Texaco Reaction
Accept 2 Billion?
Final Court Decision
Pennzoil Reaction
7
Steps to draw Influence Diagram from a Decision
Tree

• Step 3
• Connect them meaningfully but not as a flow chart

Texaco Reaction
Accept 2 Billion?
Final Court Decision
Information
Influence
Pennzoil Reaction
8
Developing the table
Write the headings using the decision tree from
left to right
9
Developing the table
Fill column 2
10
Developing the table
Fill column 3 Pennzoil reaction is valid for
only 3B counter offer from Texaco, however you
should write them for all the outcomes
11
Developing the table
Fill column 4 Court decision is valid for
Refuse as marked in circle, but write for all
the rows
12
Solving the diagram
Fill the pay off column. Solve right to left
13
Solving the diagram
Revised Payoff Table (Using Expected Values for
Court Decision) Multiply weights and values and
find the additive value function
Texaco Reaction
Accept 2 Billion?
Final Court Decision
Pennzoil Reaction
14
Solving the diagram
Texaco Reaction
Accept 2 Billion?
Final Court Decision
15
Solving the diagram
Texaco Reaction
Accept 2 Billion?
Final Court Decision
Accept Expected Payoff 2 Billion? (
Billion) Accept 2 2.0 Offer 5
4.63