Exercise 4.8 Consider the extensive game Figure 4.22. (a) How many proper subgames does the game have? (b) How many of those proper subgames are minimal? 2 1 0 2 a x d 1 b 2 03g 0 1 f 3 h 20 1 0 2 0 1 1 Figure 4.22: The game of Exercise 4.8
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- Mete is Esra's boyfriend. Esra is expecting a marriage proposal from Mete. Today is Sunday. Mete says Esra that: (1) he is going to propose Esra on Monday or Tuesday or Wednesday or Thursday or Friday, at 10:00 pm. (2) he knows right now the day when he will propose (3) but the day of proposal will be a surprise to Esra: On the day of the proposal, she would not be expecting the proposal that day. Esra says Mete that what he says is impossible. Explain why Esra is right in a few sentences.Suppose Jay has been experiencing back pain and that there are two options for back pain: Treatment Regimen Total Cost Pain Reduction Do nothing $0 0 units Cortisone injections $600 30 units Calculate the ICER between cortisone injections and doing nothing. Jay says he is willing to pay $10 for a per unit of pain reduction. Should he choose cortisone injections? Another treatment is discovered. It costs $700 and reduces pain by 25 units. Should he choose the new treatment?5. Shift-in-charge Nazar Al Rushdy: Nazar is pessimistic about the market price. What is your guidance for Nazar? The decision to employ decision trees in crucial situations has been taken by Salem Al Harthi, the plant manager. The table below presents data on demand for a duration of 6 hours along with their respective probabilities. The first row of the table provides the probability of demand for the initial three hours when a leak occurs, denoted in parentheses. Subsequently, the following three rows indicate the probabilities of high, medium, and low demand for the succeeding three hours. To illustrate, if the initial 3-hour market price was low, the probabilities of high demand, medium demand, and low demand in the next three hours are 0.2, 0.3, and 0.5, respectively. Market price High Market price Medium Initial 3-hrs (0.2) Initial 3-hrs (0.5) Market price Low Initial 3-hrs (0.3) High demand (next (0.5) (0.4) (0.2) 3 hrs) Medium demand (0.3) (0.2) (0.3) (next 3 hours) Low demand…
- 1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?
