Solving Influence Diagrams

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

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

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.

Pennzoil Decision Tree Solve right to left

Payoff 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

Payoff 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

Payoff 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

Developing the table Write the headings using the decision tree from left to right

Developing the table Fill column 2

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

Developing the table Fill column 4 Court decision is valid for Refuse as marked in circle, but write for all the rows

Solving the diagram Fill the pay off column. Solve right to left

Payoff 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

Payoff Pennzoil Reaction Solving the diagram Texaco Reaction Accept $2 Billion? Final Court Decision

Payoff Pennzoil Reaction 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

Solving Influence Diagrams