Preamble Consider the situation faced by oil giants Texaco, Getty Oil and Pennzoil during the 1980s.

In early 1984, Pennzoil had reached an agreement with Getty Oil to buy out their shares and merge. But before the deal was initialed, Texaco offered a significantly more attractive price to Getty Oil. Gordon Getty, the majority shareholder, cancelled the agreement with Pennzoil and sold to Texaco. Naturally, Pennzoil felt it had been treated unfairly and filed suit against Texaco, claiming that it had illegally interfered in the negotiations between Pennzoil and Getty. Pennzoil won its case and, in late 1985, was rewarded with an $11.1 billion ($11.1B) judgment, the largest judgment in the United States at the time. A Texas appeals court later reduced the judgment to $2 billion, but with interest and penalties, the sum was still $10.3G. James Kinnear, Texaco's CEO, said at the time that his company would have to declare bankruptcy if Pennzoil got permission from the court to secure the judgment by seizing Texaco's assets and infrastructure. In addition, Kinnear promised that he would fight, all the way to the Supreme Court if necessary, arguing that Pennzoil had not followed the financial laws of the Securities & Exchange Commission during its negotiations with Getty. In April 1987, just before Pennzoil seized its assets, Texaco offered Pennzoil $2 billion to settle the entire dispute. Hugh Liedtke, Pennzoil's CEO, said at the time that his advisors were telling him that a settlement of between $3 billion and $5 billion should be considered fair and acceptable.

Problem So Liedtke must decide whether he should accept or reject the $2B settlement offered by Texaco. If Liedtke rejects the offer, it will respond with a $5G counteroffer, which Texaco will either accept, reject, or respond in turn with a $3G counteroffer. Liedtke's advisors estimated the probabilities of these three Texaco responses to be, respectively, 0.17 (Texaco accepts the $5G offer), 0.50 (Texaco rejects the $5G offer), and 0.33 (Texaco responds with a $3G counteroffer). If no counteroffer is accepted, the case will be settled by an arbitration tribunal, which will decide in one of three ways: completely in favor of Pennzoil ($10.3G settlement), completely in favor of Texaco ($0 settlement), or partially in favor of Pennzoil ($5G settlement). Liedtke's advisors estimated the probabilities of these three judgments to be, respectively, 0.20, 0.30, and 0.50.

Structure and solve Liedtke's decision tree to determine his optimal strategy. Also, comment briefly on two assumptions of the decision trees that become less realistic in this context.