Decision tree, decision strategy, and probability

James Kildare claims to have injured his back as a result of falling out of a chair. James, who has a PhD in physics, but can’t find a job because of government budget cuts, had been hired to play a doctor in a hastily produced video. The producer of the video wanted to hire a PhD, since they can legitimately be called “doctor,” and are cheap. Not having a real job, James cannot afford medical insurance and thus is looking for someone to sue. The producer of the video has fled the country, the chair is manufactured in the Kaesong Industrial Region of North Korea, and he can’t find out who commissioned the video and forced the rushed schedule. Thus, he has filed a lawsuit against the only deep-pocket he could find; Roland Wellington who owns the company that imports these chairs and stamps their logo on them. He is asking for damages of $1,500,000. James claims that the chair frame was made from recycled soda cans and that his fall could have been prevented if Mr. Wellington had not circumvented chair safety requirements by making huge contributions to the political campaign of Congressman Ned Froemer who chairs the committee responsible for oversight of the government agency charged with regulating office chairs. Mr. Wellington notified his insurance company, Axis Insurance, of the lawsuit. Axis must defend Mr. Wellington and decide what action to take regarding the lawsuit.

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Some depositions and a series of discussions have taken place between both sides. As a result, James offered to accept a settlement of $750,000. Thus, one option is for Axis to pay James $750,000 to settle the claim. Axis is also considering making James a counteroffer of $400,000 in the hope that he will accept a lesser amount to avoid the time and the cost of going to trial. Dr. Kildare’s PhD thesis was in the metallurgy of recycled soda cans, and thus Axis Insurance believes that James may have a strong case since he can act as his own expert witness. Axis is also concerned that James may reject their counteroffer and request a jury trial. Axis’ lawyers spent some time exploring James’ likely reaction if they make a counteroffer of $400,000.

The lawyers concluded that it is adequate to consider three possible outcomes to represent James’ possible reaction to a counteroffer of $400,000. (1) James will accept the counteroffer and the case will be closed. (2) James will reject the counteroffer and elect to have a jury decide the settlement amount, or (3) James will make a counteroffer to Axis of $600,000. If James does make a counteroffer, Axis decided that they will not make additional counteroffers. They will either accept James’ counteroffer of $600,000 or go to trial.

If the case goes to jury trial, Axis considers three outcomes possible: (1) The jury may reject James’ claim and Axis will not be required to pay any damages; (2) The jury will find in favor of James and award him $750,000 in damages or (3) The jury will conclude that James has a strong case and award him the full amount of $1,500,000.

Key considerations as Axis develops its strategy for disposing of the case are the probabilities associated with James’ response to an Axis counteroffer of $400,000 and the probabilities associated with the three possible trial outcomes. Axis’ lawyers believe the probability that James will accept the counteroffer of $400,000 is 0.1; that the probability that James will reject the counteroffer of $400,000 is 0.4; and the probability that James will, himself, make a counteroffer to Axis of $600,000 is 0.5. If the case goes to court, they believe that the probability the jury will award James damages of $1,500,000 is 0.3; the probability that the jury will award James damages of $750,000 is 0.5; and the probability that the jury will award James nothing is 0.2.

Perform an analysis of the problem facing Axis Insurance and prepare a report that summarizes your findings and recommendations. Be sure to include: (1) a decision tree; (2) a recommendation regarding whether Axis should accept James’ initial offer to settle the claim for $750,000; (3) a decision strategy that Axis should follow if they decide to make James a counteroffer of $400,000; and (4) compute the probability for each final outcome using your recommended strategy (that is, develop a risk profile of your recommended strategy).