$12.$S$2.$ Settle or Go to Trial

Meredith Delgado owns a small firm that has developed software

for organizing and playing music on a computer. Her soft$-$

ware contains a number of unique features that she has patented,

so her company's future has looked bright.

However, there now has been an ominous development. It appears

that a number of her patented features were copied in similar

software developed by MusicMan Software, a huge software

company with annual sales revenue in excess of $$1$ billion.

Meredith is distressed. MusicMan Software has stolen her ideas

and that company's marketing power is likely to enable it to capture

the market and drive Meredith out of business.

In response, Meredith has sued MusicMan Software for patent

infringement. With attorney fees and other expenses, the cost of going

to trial $($win or lose$)$ is expected to be $$1$ million. She feels that she

has a $60$ percent chance of winning the case, in which case she would

receive $$5$ million in damages. If she loses the case, she gets nothing.

Moreover, if she loses the case, there is a $50$ percent chance that the

judge would also order Meredith to pay for court expenses and lawyerfees for MusicMan $($an additional $$1$ million cost$).$ MusicMan Soft$-$

ware has offered Meredith $$1\mathrm{.}5$ million to settle this case out of court.

a$.$ Construct and use a decision tree to determine whether

Meredith should go to court or accept the settlement offer,

assuming she wants to maximize her expected payoff.