Francisco and Priya have developed an innovative new product and applied for a patent for it. They estimate that there is an 80% chance that their patent will be approved by the US Patent Office.

They also presented their product to ITNET, a large corporation, after having ITNET sign a confidentiality agreement. Yesterday, ITNET announced a new product suspiciously similar to Francisco and Priya’s. Francisco’s first impulse was to sue ITNET immediately. However, Priya feels that they should wait until they have received notification of whether their patent is approved. Priya reasoned that their case would be much stronger if they had a patent for their product.

Suppose that Francisco and Priya have a 90% chance of winning a lawsuit against ITNET if their patent application is approved, and that they still have a 60% chance of winning such a lawsuit even while their patent application is under review. However, if their patent application is not approved, the chance of winning the lawsuit would drop to 40%.

If they sue ITNET immediately (while the patent application is still under review), there is a 70% chance that ITNET would settle out of court for $400,000, and a 30% chance that ITNET would not settle out of court and the suit would proceed to trial.

If Francisco and Priya win at a trial, the award would be $1 million (if they lose they get nothing). They estimate that the legal costs of a trial would be $100,000, regardless of whether they win or lose. If they wait until after the patent application has been reviewed to file suit, there is no chance that ITNET would settle out of court and the suit would go straight to trial.

(a) Use a decision tree to determine what Francisco and Priya should do (i.e. when they should file their lawsuit). State the optimal decision strategy and its expected value.

(b) Draw a risk profile for the optimal decision strategy.