In early 1984, Pennzoil and Getty Oil agreed to the terms of a merger. Before any formal documents could be signed, however, Texaco offered Getty Oil a substantially better price, so 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 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 the Security and Exchange Commission's 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, faced the choice of whether to accept the Texaco offer. His advisors were telling him that a settlement of between $3 and $5 billion would be fair, so one of his options was to make a counteroffer of $5 billion. If Liedtke were to counteroffer, assume Texaco would be twice as likely to refuse as accept the $5 billion counteroffer. If Texaco would refuse, the case would go to court, where the judge would award Pennzoil $10.3 billion, or reduce the award to $5 billion, or award Pennzoil nothing. The probability that the judge would award Pennzoil nothing is about 50 percent, while the other outcomes were thought to be equally likely (25 percent probability).2
a. What is the best decision for Liedtke, and what is his expected payoff?
b. What is the expected payoff if Pennzoil counteroffers and Texaco refuses? Why is the expected payoff to the counteroffer higher than this?
c. Consider the probability that the judge would award Pennzoil nothing. How high would this probability have to go before the best decision would be to accept the $2 billion offer? (Assume that the probabilities of the other two outcomes are always equal.)