Problem sets for Microeconomics II [110051-0471]

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7 Game theory Exercise 7.1. Firms M and N compete for a market and must independently decide how much to advertise. Each can spend either $10 million or $20 million on advertising. If the firms spend equal amounts, they split the $120 million market equally. (For instance, if both choose to spend $20 million, each firm’s net profit is 60 – 20 = $40 million.) If one firm spends $20 million and other $10 million, the former claims two thirds of the market and the latter one-third. a. If the firms act independently, what advertising level should each choose Explain. Is a prisoner’s dilemma present b. Could the firms profit by entering into an industry-wide agreement concerning the extent of advertising Explain. Exercise 7.2. A firm sells two goods in a market consisting of three types of consumers. The table shows the values consumers place on the goods. The unit cost of producing each good is $5. Good Consumers X Y A 13 6 B 7 11 C 15 2 Find the optimal prices for (a) selling the goods separately, (b) pure bundling, and (c) mixed bundling. Which pricing strategy is most profitable Exercise 7.3. Find all Nash equilibriums in the game of two banks, whose management considers selling to debtors their liabilities for the discounted price. Bank II S NS Bank I S 6,6 6,11 NS 11,6 6,6 Exercise 7.4. There are three payoff tables given. a. Identify the equilibrium outcome(s) in each of the three payoff tables. I. C 1 C 2 R 1 12,10 10,4 R 2 4,8 9,6 II. C 1 C 2 R 1 12,10 4,4 R 2 4,4 9,6 18 III. C 1 C 2 R 1 12,10 4,4 R 2 4,-100 9,6
. In each table, predict the exact outcome that will occur and explain your reasoning c. In table III, suppose the column player is worried that the row player might choose R 2 (perhaps a one-in-ten chance). Given the risk, how should the column player act Anticipating the column player’s thinking, how should the row player act Exercise 7.5. Two firms dominate the market for surgical sutures and compete aggressively with respect to research and development. The following payoff table depicts the profit implications of their different R&D strategies. a. Suppose that no communication is possible between the firms; each must choose its R&D strategy independently of the other. What actions will the firms take, and what is the outcome b. If the firms can communicate before setting their R&D strategies, what outcome will occur Explain. Firm B’s R&D Spending Low Medium High Firm A’s R&D Spending Low 8,11 6,12 4,14 Medium 12,9 8,10 6,8 High 11,6 10,8 4,6 Exercise 7.6. One way to lower the rate of auto accidents is strict enforcement of motor vehicle laws (speeding, drunk driving, and so on). However, maximum enforcement is very costly. The following payoff table lists payoffs of a typical motorist and a town government. The motorist can obey or disobey motor vehicle laws, which the town can enforce or not. Town Enforce Don’t Enforce Motorist Obey 0,-15 0,0 Don’t Obey -20,-20 5,-10 a. What is the town’s optimal strategy What is the typical motorist’s behavior in response b. What if the town could commit to a strict enforcement policy and motorists believed that this policy would be used Would the town wish to do so 19
Page 1 and 2: Problem sets for Microeconomics II
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Problem sets for Microeconomics II [110051-0471]

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