Managerial Economics1. Find all Nash Equilibrium of the following game (Hint: specify the order in which you eliminatedominated strategies):Players 2Actions V W X Y ZA 4 , -1 3 , 0 -3 , 1 -1 , 4 -2 , 01 B -1 , 1 2 , 2 2 , 3 -1 , 0 2 , 5C 2 , 1 -1 , -1 0 , 4 4 , -1 0 , 2D 1 , 6 -3 , 0 -1 , 4 1 , 1 -1 , 4E 0 , 0 1 , 4 -3 , 1 -2 , 3 -1 , -12. Nikon and Canon both produce high end digital cameras. They can each chose high or low levelsof advertising. The payoff matrix is as follows:Players NikonLow HighCannon Low 12, 13 11, 12High 13, 12 12, 11Describe the equilibrium strategies for each firm. Do they have dominant strategies?3. Firm A currently monopolizes its market and earns profits of $10 million. Firm B is a potentialentrant that is thinking about entering the market. If B does not enter the market, it earnsprofits of $0, while A continues to earn $10 million. If B enters, then A must choose betweenaccommodating entry and fighting. If A accommodates it earns $5 million and B earns $5 million.If it fights, both firms lose $5 million.a. Draw the game in extensive form and predict the outcome.b. Now suppose the decision of firm B is reversible in the following way. After B enters themarket and A has decided to fight or accommodate, B can choose to remain in themarket or exit. All payoffs from the above game remain the same, however, if B decidesto exit the market then B suffers a loss of $1 million while A regains its old profits of $10million. Draw the game in extensive form and predict the outcome.4. Consider a father who is trying to discipline his child. The father insists that the child must go tovisit his grandmother. The child wants to go to the movies with a friend. If the child and fatherboth go to visit the grandmother they each receive 1 unit payoff. If the child refuses to go andthe father punishes the child the child receives one unit of utility and the father receives 1 unitof utility. If the child goes to the movie and the father does not punish then the child receives 2units of utility and the father receives none.a. Draw the game in matrix form (hint: there will be one empty entry).b. Draw the game in extensive form.c. Solve the game using backward induction.5. The CEO of a car company says that she is indifferent between the certainty of receiving $7,500and a gable where there is a 50% chance of receiving $5,000 and $10,000. Also she is indifferentbetween having $10,000 and a 50% gamble between $7,500 and $12,500.a. Draw four points on the utility function of the CEO.b. Does she seem to be risk averse, risk loving, or risk neutral? Explain.6. Suppose that you have an option to purchase a particular piece of land and must decide if youwant to drill on the land before the expiration of the option or give up your rights. The cost ofdrilling is $200,000. If there is oil you will receive $1,000,000, if not you receive nothing.a. Construct a decision tree to represent your decision.b. Can you tell if you should drill based on the available information. Why or why not?c. You believe that the probability of finding oil if you drill is 25%. Can you now decide ifyou should drill? Why or why not?d. Suppose that you are a risk lover. Should you drill? Why or why not?e. Suppose you are risk neutral, should you drill? Why or why not?
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