ECON7070 TUTORIAL 2
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ECON7070
TUTORIAL 2
Question 1. An oil drilling company must decide whether or not to engage in a new drilling venture. The cost of drilling is 1 million. The company will learn whether or not there is oil on the site only after drilling has been completed and all drilling costs have been incurred. If there is oil, operating profits (i.e., revenue minus cost of extracting and selling oil, not including the drilling cost) are estimated at 4 million. If there is no oil, there will be no future profits. With probability 0.5, a new 50% tax on the operating profits from drilling will be introduced. Let p denote the likelihood that drilling results in oil and assume the company has a von Neuman-Morgenstern utility function.
(a) The company estimates that p = 0.6. What is the expected utility of drilling? Should the company go ahead and drill?
(b) To be on the safe side, the company hires a specialist to come up with a more accurate estimate of p. What is the minimum value of p for which it would be the company’s best response to go ahead and drill?
Question 2. Represent the following strategic interaction using a payoff matrix.
A couple (a she and a he) is going out for an evening. They have two options: watching a football match or going to an opera. Unfortunately his mobile phone runs out of battery. Unable to reach each other, each of them needs to go to one of the possible venues without knowing where his/her partner has gone. Spending the evening alone (whether at the football or the opera) is the worst outcome for both of them. Conditional on going out together, she prefers football to opera while he prefers opera to football. Make “she” Player 1 when writing the payoff matrix.
Question 3. Three firms use water from a lake. Each firm has two possible actions: treat sewage (T) or dump sewage (D). If no firms or only one firm dumps sewage, the lake remains clean. If two or more firms dump sewage, the lake becomes polluted. Each firm gets a revenue of 4 if the lake is clean, and a revenue of 1 if the lake is polluted. The cost of treating sewage is 1. There is no cost to dumping sewage. Each firm’s payoff is given by its revenue minus the sewage treatment cost, if any.
(a) Describe this situation as a normal form game using payoff matrices.
(b) Is there a (strongly or weakly) dominated action for any player? If yes, which one? If no, explain why.
2023-03-10