Decision Analysis Homework

Problem $1.$

Meredith Delgado owns a small firm that has developed software for organizing and playing music on a computer. Her software 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 $$2\mathrm{.}25$ million. She feels that she has a $40\%$ chance of winning the case, in which case she would receive $$7\mathrm{.}25$ million in damages. If she loses the case, she has to pay $$2\mathrm{.}25$ million in cost$.$ IF she settles before trial, she obtains $$1M.$ Construct a model using the Bayes' Decision Rule. Keep in mind that the winnings is based upon profit after attorneys and court costs have been settled.

A$)$ Construct a Table using:

a$.$ Prior Probabilities of Winning $($in percentage, starting at $38\%$ to $48\%)$

b$.$ Prior Probabilities of Losing $($in percentage, compared to Winning side$)$

c$.$ Go to Trial $($EP$)$

d$.$ Settle $($EP$)$

e$.Y$ or $N$ for Decision to go to trial.

B$)$ Put your Prior Probability values to the values where EP for going to trial is at least $$10,000$ more than settling.