Question: At the end of the year, Konstantin plans to graduate and find a job. He is currently evaluating several job prospects, and his choice has come down to one of two. He will either work for Clairvoyant Consultants, Inc. (CCI), or for the Wizard of Wall Street and Company (WWS & Co.).
If he goes to work for CCI, Konstantin will start out as a driver for their famous Field Action Minivan. He has been promised a starting salary of $25,000/year. CCI has a firm rule that everyone must start out as a driver in the Bay Area for three weeks before getting a permanent assignment.
The position of driver has long been known to carry a great deal of prestige at CCI, and Konstantin figures that starting out as a driver, he has a 90% chance of being promoted to some better position after only three weeks on the job. Unfortunately, he must sign a one-year contract with CCI before he finds out whether or not he'll get the promotion, and since CCI is badly in need of drivers, there is still that 10% chance that they'll keep him there for the rest of this year.
Despite that, Konstantin suspects that there is a 30% chance of being promoted to Associate Clairvoyant. Given that he is promoted, he suspects there is a 50-50 chance that he will be sent to either CCI's San Francisco office or their San Jose office. The San Francisco office pays its Associate Clairvoyants $42,000/year, while the San Jose office pays its Associate Clairvoyants on a very strange commission schedule. If they bring in a new client, San Jose's Associate Clairvoyants are paid $53,000/year, but if they do not bring in a new client, they are only paid $32,000/year. Konstantin figures there is a 40% chance that, as an Associate Clairvoyant, he could bring in a new client
Having listened closely to the rumor mills, Konstantin discovers that CCI is desperately in need ofpeople to start up a new office in Osaka, Japan. Being fluent in Japanese, he suspects there is a 60% chance that CCI will choose to send him to Japan rather than keeping him in the bay area. But once he gets there, he doesn't know whether he will be an Associate Clairvoyant or a Senior Clairvoyant. After consulting with Blair's probability wheel, Konstantin determines that if he is sent to Osaka, there is a 85% chance that he'll be made a Senior Clairvoyant, and only a 15% chance that he will be an Associate Clairvoyant. Japanese Senior Clairvoyants are paid $95,000/year, but Associate Clairvoyants are only paid $35,0()0/year. The Wizard of Wall Street & Company has offered Konstantin $60,000/year to work in New York City. However, there is no chance of promotion once he gets there.
Konstantin decides that he would be equally happy working in any of these cities. His only concern is for his salary level at the end of the first year. He doesn't care about anything after the first year-he plans to join a Tibetan monastery and will relinquish all worldly possessions at that time. After pondering his predicament for several hours, Konstantin comes up with the following information. He wishes to follow the delta property over all the prospects in his problem. He considers a deal for equal chances of either $100,000 or nothing to be worth about $38,000. He considers that same deal for $100,000 or nothing, with a 75% probability of getting $100,000, to be worth about $64,000.
Konstantin's friend has changed his mind; she will not allow Konstantin to choose which uncertainty she reveals. Konstantin is uncertain which of his uncertainties his friend will reveal, and assigns equal probabilities to each of his four uncertainties (Driver/Bay Area/Japan, San Jose/San Francisco, Finding a new client in San Francisco, Being promoted to Senior Clairvoyant in Japan). Draw his new decision diagram, and determine his PTBP for his friend's services.