$15.[20$ pts$]$ The Texaco vs$.$ 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 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 $\backslash (\backslash$$ $11\mathrm{.}1\backslash )$ billion, the largest judgment ever in the United States at that time. A Texas appeals court reduced the judgment by $\backslash (\backslash$$ $2\backslash )$ billion, but interest and penalties drove the total back up to $\backslash (\backslash$$ $10\mathrm{.}3\backslash )$ billion. James Kinnear, Texaco's chief executive officer, had said that Texaco would file for bankruptcy if Pennzoil obtained court permission to secure the judgment by filing liens against Texaco's as$-$sets. Furthermore, Kinnear had promised to fight the case all the way to the U$.$S$.$ Supreme Court if necessary, arguing in part that Pennzoil had not followed Security and Exchange Commission regulations in its negotiations with Getty. In April $1987,$ just before Pennzoil began to file the liens, Texaco offered to pay Pennzoil $\backslash$$$2$ billion to settle the entire case. Hugh Liedtke, chairman of Pennzoil, indicated that his advisors were telling him that a settlement between $\backslash (\backslash$$ $3\backslash )$ and $\backslash (\backslash$$ $5\backslash )$ billion would be fair.

Assuming that the decision tree of this problem is shown below $($the number is in the parentheses is the probability$).$

a$.$ Using the expected value theory, determine which choice or decision Liedtke should make.

b$.$ Suppose that Liedtke's utility function is shown in the table below.

Utility Function

b$\mathrm{.}1$Graph Liedtke's utility function and determine Liedtke's attitude toward risk.

b$\mathrm{.}2$With Liedtke's risk attitude determined in part $1,$ what strategy should he pursue?