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Lecture 10: Oligopoly Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects, unless at least one confesses. The police hold the suspects in separate cells and explain the consequences that will follow from the actions they could take. If neither confesses, then both will be convicted of a minor offense and sentenced to two years in jail. If both confess, then both will be sentenced to jail for 10 years. Finally, if one confesses but the other does not, then the confessor will serve only 1 year but the other will be sentenced to 20 years in jail – 10 for the crime and a further 10 for obstructing justice. The possible outcomes are depicted below. Prisoner 2 (Sally) Confess Don't Confess Prisoner 1 Confess M: -10; S: -10 M: -1; S: -20 (Mike) Don't Confess M: -20; S: -1 M: -2; S: -2 What would you do? A dominant strategy is a strategy that works better than any other strategy regardless of what the other player is doing. The Nash Equilibrium is where each player is doing the best that they can given what the other player is doing. The Stackelberg Equilibrium is the Nash Equilibrium to a sequential move game. The dominant strategy in the prisoner’s dilemma is to confess. The Nash Equilibrium is for both players to confess. If each player has a dominant strategy, then the dominant strategies will indicate the Nash Equilibrium. However, it is possible to have a Nash Equilibrium where the players have no dominant strategies. Now, show this as a simultaneous move game tree. Prisoner 1 Confess Not Confess Prisoner 2 Confess Not Confess Confess Not Confess (prisoner 1): 10 years 1 year 20 years 2 years (prisoner 2): 10 years 20 years 1 year 2 years David Wessel, in his 2002 Wall Street Journal article, “The Civilizing Effect of the Market,” attempts to determine whether those in market economies are more generous. To do this, he sets up an experiment with two consumers. He gives the first consumer $100.00. The first consumer must decide how much of the $100.00 to give to consumer two. Then, consumer two either accepts or rejects the offer. If consumer two rejects the offer, then both consumers get nothing. However, if consumer two accepts consumer one’s offer, then they both receive money according to consumer one’s proposed division. Let the following payoff matrix depict the game. In this setup, consumer one may give consumer two either $1.00 or $50.00. Then, consumer two may either accept or reject the offer. Player one Offer $1.00 Offer $50.00 Accept one$99two$1 one$two$ Player two Reject one$two$one$two$ a) Does consumer one have a dominant strategy? If so, what is it? b) Does consumer two have a dominant strategy? If so, what is it? c) Assume consumer one moves first. Identify the Stackelberg Equilibrium. Surprisingly, Wessel found that those in capitalism were more generous than those in Marxist economies. Characteristics of Oligopoly: 1. Many buyers and a few sellers 2. Homogeneous product 3. There may or may not be entry 4. Imperfect Information Suppose the demand for oil is D: P = 100-QD, and that there are two oil companies: Ewing and Wesstar Oil. Let MC be constant with no fixed costs so that MC=ATC= $20.00. These two oil companies first have the option of producing either 20 or 25 units of oil. Ewing Oil 20 25 E: 800 E: 875 20 W: 800 W: 700 E: 700 E: 750 Wesstar Oil 25 W: 875 W: 750 2 The dominant strategies are for each company to produce 25 barrels of oil. This strategy works better than producing 20 barrels of oil regardless of what the rival firm does. The Nash Equilibrium is for each company to produce 25 barrels of oil. In this box, neither player wants to change their behavior given what their rival firm is doing. Now suppose that they have a third option: to produce 40 units of oil. Ewing Oil 20 25 40 E: 800 E: 875 E: 800 20 W: 800 W: 700 W: 400 E: 700 E: 750 E: 600 Wesstar Oil 25 W: 875 W: 750 W: 375 E: 400 E: 375 E: 0 40 W: 800 W: 600 W: 0 The companies no longer have dominant strategies. What works best hinges on what the rival firm does. However, the Nash Equilibrium is for each company to produce 25 barrels of oil. If this were a sequential move game where Ewing Oil moves first, then the Stackelberg Equilibrium would be for Ewing to produce 40 barrels and Wesstar to produce 20 barrels. Note that it is an advantage to move first. By moving first, Ewing Oil has higher profits than if they moved second or simultaneously with Wesstar. Let demand be D: P = 200 – Q and MC = ATC = 10 with four firms: Ewing Oil Wesstar Oil Barnes-Wentworth Oil People’s Oil Maximize profits by picking the best output level across 3 periods. Ewing Wesstar Barnes-Wentworth Peoples Period 1 Period 2 Period 3 Now consider an example of entry. Suppose Boeing is the only airplane maker. Demand for airplanes is D: P = 200 – Q with constant MC = 20. Boeing can produce 45, which will maximize profits, but Planes Inc., may enter the industry and also produce 45. To keep Planes, Inc. out, Boeing is also considering producing 140. Thus, Planes Inc.,’s other option is not to enter (produce 0). 3 Boeing 45 140 B: 6075 B: 5600 0 P: 0 P: 0 B: 4050 B: -700 Planes Inc. 45 P: 4050 P: -225 What is each firm’s dominant strategy? What is the Nash Equilibrium? Now suppose that Boeing moves first in a sequential move game. Find the Stackelberg Equilibrium. Boeing 45 140 Planes, Inc. 0 45 0 45 (Boeing): $6,075 $4,050 $5,600 $-700 (Planes): $0 $4,050 $0 $-225 Now consider an example of cooperation. In this example, suppose Iraq and Kuwait are the only producers of oil. To maximize profits, the two oil-producing nations agree to maximize joint profits as a monopoly would and then divide such profits. That is, Iraq and Kuwait agree to form a cartel. D: P = 100 – ½ Q and MC = ATC = 10. Iraq 45 50 I: 2025 I: 2125 45 K: 2025 K: 1912.5 I: 1912.5 I: 2000 Kuwait 50 K: 2125 K: 2000 Find the Nash Equilibrium. Is the cartel agreement sustainable? Second Game: 4 Five firms must pick a high (cartel) price or a low price. The game is played for three periods. Firms may discuss strategies. Company with the most profits gets the extra credit. In the case of a tie, divide the extra credit among the winners. Number of Number of Profit for Each Profit for Each High-Priced Firms Low-Priced Firms High-Priced Firm Low-Priced Firm 0 5 - 50 1 4 20 70 2 3 40 90 3 2 60 110 4 1 80 130 5 0 100 - 5 Problem Set 10: Oligopoly 1. Let Procter and Gamble (P&G) and SmithKline Beecham (SKB) be the only two firms that produce toothpaste, making this industry a duopoly. Proctor and Gamble and SmithKline Beecham may each produce either 40 or 50 units of output. The following payoff matrix shows the profits each firm would earn for these levels of output. SmithKline Beecham QSK B= 40 QSK B =50 QP&G=40 SKBPGSKBPG Proctor and Gamble QP&G=50 SKBPGSKBPG a) What is Procter and Gamble's dominant strategy? b) What is SmithKline Beecham's dominant strategy? c) What is the Nash Equilibrium of this game for this duopoly? d) Depict this game with a decision tree below. Then, identify the terminal node that correctly represents the quantity each firm in the duopoly will produce in equilibrium. 2. Suppose Iran and Iraq each produce crude oil and both want a high market price for crude oil to create larger profits. To keep the market price for oil high, Iran and Iraq have agreed to keep production low: Iran and Iraq have each agreed to only produce 35 units of crude oil. Now, Iran and Iraq must each decide whether to honor this agreement and cooperate. Honoring the agreement means producing 35 units of crude oil. However, each country also has the option of secretly breaking the agreement and producing 50 units of output to earn higher profits. Suppose Iran and Iraq must each decide how much crude oil to produce simultaneously. Thus, when Iran decides how much to produce, it doesn’t know whether Iraq is honoring the agreement. Similarly, Iraq must decide how much to produce without knowing how much Iran is producing. This situation is depicted using a payoff matrix below. Iran Q = 35 Q =50 Q=35 IRANiRAQIRANIRAQ Iraq Q=50 IRANIRAQIRANIRAQ a) Does Iran have a dominant strategy? If so, what is it? b) Does Iraq have a dominant strategy? If so, what is it? c) Find the Nash Equilibrium for this game. 6 3. Consider the market for baseball caps. You are the CEO of a company, which is the only producer of baseball caps. Initially, you had been maximizing profits by producing quantity Q=90. However, a new firm is considering entering the baseball cap market to get a share of the positive economic profits being earned. The following decisions must be made: you must decide whether to continue producing quantity Q=90 (the profit maximizing level of production for a monopoly) or to produce Q=150 (you would produce 150 baseball caps in an effort drive market price down so low that the new firm would rather not enter the cap making industry); the new firm must decide whether to enter the market and produce Q=50 or not enter the market and produce nothing (Q=0). We are therefore assuming that you can produce Q=90 or Q=150 and the new firm can produce Q=0 or Q=50. This situation is depicted using a payoff matrix. For parts (a) – (c), assume you and the new firm must decide how much to produce simultaneously. You QY= 90 QY =150 QNF=0 YNFYNF New Firm QNF=50 YNFYNF a) Do you have a dominant strategy? If so, what is it? b) Does the new firm have a dominant strategy? If so, what is it? c) Find the Nash Equilibrium for this game. Now suppose your firm (being more established and trusted by the consumer) is the dominant firm in the industry such that you decide how much to produce first and the new firm decides how much to produce second. d) Find the Stackelberg Equilibrium for this game. State how much you and the new firm produce. 4. The Windows operating system from Microsoft, Inc. runs about 90% of the world’s personal computers, so it is natural to think that Microsoft has a monopoly in the market for operating systems. According to economist Richard Schmalensee, an expert on oligopoly and monopoly, Microsoft’s profit-maximizing monopoly price is between $900 and $2,000. That’s the amount Microsoft would charge if it acted like a regular monopolist. However, Microsoft has tended to charge only $99 for Windows. Perhaps Microsoft is an insecure monopolist and picks a low price to discourage entry and preserve its monopoly. In other words, if Microsoft charged $2,000 for its operating system, there would be an incentive for other firms to develop alternative operating systems. Suppose that the market for operating systems is initially a monopoly (Microsoft is the monopoly) with the potential for a second firm to enter the industry. Suppose Microsoft can charge a price of either $99 or $900 for its operating system. Suppose a second firm has three options: enter the industry and charge $99, enter the industry and 7 charge $900, and not enter the industry. The profits that would result from these outcomes are presented in a payoff matrix below. Microsoft (M) P=$99 P=$900 Enter, P=$99 M=5 M=0 NF=5 NF=10 New Firm (NF) Enter, P=$900 M=10 M=50 NF=0 NF=50 No Entry M=10 M=100 NF=0 NF=0 Assume that Microsoft and the New Firm move simultaneously. a) Does Microsoft have a dominant strategy? If so, what is it? b) Does the New Firm have a dominant strategy? If so, what is it? c) Find the Nash Equilibrium for this game. Actually, there are two. Find both of them. Now assume that Microsoft moves first and that the New firm moves second. d) Find the Stackelberg Equilibrium to a sequential-move game. 5. Suppose that the market for crude oil is a duopoly comprised of two oil-producing nations -- Saudi Arabia (SA) and Qatar (Q). Since Saudi Arabia is a much larger oil- producing nation than Qatar, suppose that Saudi Arabia is the industry leader. Therefore, Saudi Arabia gets to pick how much to produce first. Then, Qatar finds out how much Saudi Arabia has produced and picks an output level. Assume that Saudi Arabia’s output choices are 100 and 200 and that Qatar’s output choices are 3 and 5. This situation is depicted using a payoff matrix below. Saudi Arabia Q = 100 Q =200 Q=3 SAQSAQ Qatar Q=5 SAQSAQ a) Find the Stackelberg Equilibrium. Now assume that Saudi Arabia and Qatar move simultaneously. That is, they decide to produce without knowing how much each other are producing. b) Does Saudi Arabia have a dominant strategy? If so, what is it? c) Does Qatar have a dominant strategy? If so, what is it? d) Find the Nash Equilibrium for this game. 8 Answer Key 10: Oligopoly Answer to question 1: SmithKline Beecham QSK B= 40 QSK B =50 QP&G=40 SKBPGSKBPG Proctor and Gamble QP&G=50 SKBPGSKBPG a) The dominant strategy is to produce output of 50. This is the dominant strategy because Proctor and Gamble’s profits will be higher by producing 50 regardless of what SmithKlein Beecham does. b) The dominant strategy is to produce output of 50. This is the dominant strategy because SmithKlein Beecham’s profits will be higher by producing 50 regardless of what Proctor and Gamble does. c) The Nash Equilibrium is QSKB = 50 and QPG = 50. This is the only output level for which both firms do not want to alter their behavior – that the definition of equilibrium: no more changes. If both firms produced output of 40, then profits would be higher, but his would not be an equilibrium because each would want to increase production to 50 to increase profits (from 3200 to 3500). Given that Proctor and Gamble produces 50, SmithKlein Beecham maximizes profits by producing QSKB = 50. There is no pressure for SmithKlein Beecham to change its behavior. Given that SmithKlein Beecham is producing 50, Proctor and Gamble maximizes profits by producing 50. There is no pressure for Proctor and Gamble to change its output level. This can’t be said for any other output combination, so it’s the Nash Equilibrium. SmithKlein Beecham 40 50 Proctor and Gamble 40 50 40 50 (PG): 3200 3500 2800 3000 (SKB): 3200 2800 3500 3000 The dotted lines indicate that this is a simultaneous move game. Proctor and Gamble and SmithKlein Beecham do not know what each other have selected to produce. 9 The Nash Equilibrium is QPG = 50 and QSKB = 50. There, there is no motivation for either firm to change its behavior. Answer to question 2: Iran Q = 35 Q =50 Q=35 IRANiRAQIRANIRAQ Iraq Q=50 IRANIRAQIRANIRAQ a) Iran has a dominant strategy: Iran should produce Q=50 because that will bring about the largest profits, regardless of what Iraq does. b) Iraq also has a dominant strategy: if Iran produces Q=35, then Iraq should produce Q=50, and if Iran produces 50, then Iraq would optimally produce Q=50. So, Iraq’s dominant strategy is also to produce Q=50. c) The Nash Equilibrium of a simultaneous move game has Iran producing Q=50 and Iraq producing Q=50. At those levels of production each country is doing the very best that it can, given what the rival country is doing. Neither Iran nor Iraq can change their behavior to make themselves better off when at the Nash Equilibrium. So, the cooperation didn’t work: they broke the agreement. Answer to question 3: You pick the column and the new firm picks the row. You QY= 90 QY =150 QNF=0 YNFYNF New Firm QNF=50 YNFYNF a) You have a dominant strategy: produce Q=90 because that will bring about the largest profits, regardless of what the new firm does. b) The new firm does not have a dominant strategy: if you produce Q=90, then the new firm should produce Q=50; however if you produce 150, then the new firm would optimally produce Q=0. c) The Nash Equilibrium of a simultaneous move game has you producing Q=90 and the new firm producing Q=50. At those levels of production each player is doing the 10 very best that it can, given what its rival firm is doing. Neither you nor the new firm can change your behavior to make yourself better off when at the Nash Equilibrium. d) Now you decide how much to produce first. If you produce Q=90, then the new firm will pick Q=50 and your profits will be 3,600. If you produce Q=150, then the new firm will not enter the market, resulting in profits of 4,500 for you. Because 4,500 is greater than 3,600, you will produce Q=150. The Stackelberg Equilibrium is Q=150 for you and Q=0 for the new firm. Notice that the Stackelberg Equilibrium results in greater profits for your firm when compared to the Nash Equilibrium. From this result we conclude that it is an advantage to move first. Answer to question 4. a) Microsoft does not have a dominant strategy. b) The New Firm does not have a dominant strategy. c) There are two Nash Equilibria. They are (i) Microsoft to charge P=$99 and the New Firm to enter and also charge P=$99, and (ii) Microsoft to charge P=$900 and the New Firm to enter and also charge P=$900. d) The Stackelberg Equilibrium is for Microsoft to charge a price of P=$900 and for the New Firm then to enter and charge a price of P=$900. This gives Microsoft and the New Firm profits of $50. Conversely, notice that if Microsoft had moved first by selecting a price of P=$99 then the New Firm would have maximized profits by entering and picking a price of P=$99. This would have given Microsoft profits of only $5. So, Microsoft can reason that if they move first and pick P=$900, their profits will be $50, which is greater than moving first and picking P=$99 with profits of $5. Given that Microsoft picks P=$900, the New Firm maximizes profits by moving second and picking P=$900 too. Answer to question 5: a) The Stackelberg Equilibrium is for Saudi Arabia to produce Q=100 and for Qatar to produce Q=5. b) Saudi Arabia’s dominant strategy is to produce Q=100. c) Qatar does not have a dominant strategy. d) The Nash Equilibrium is Q=100 for Saudi Arabia and Q=5 for Qatar. 11

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