Managerial Economics Study Set 8

Business

Quiz 13 :

Best-Practice Tactics: Game Theory

Quiz 13 :

Best-Practice Tactics: Game Theory

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Suppose that two mining companies, Australian Minerals Company (AMC) and South African Mines, Inc. (SAMI), control the only sources of a rare mineral used in making certain electronic components. The companies have agreed to form a cartel to set the (profit-maximizing) price of the mineral. Each company must decide whether to abide by the agreement (i.e., not offer secret price cuts to customers) or not abide (i.e., offer secret price cuts to customers). If both companies abide by the agreement, AMC will earn an annual profit of $30 million and SAMI will earn an annual profit of $20 million from sales of the mineral. If AMC does not abide and SAMI abides by the agreement, then AMC earns $40 million and SAMI earns $5 million. If SAMI does not abide and AMC abides by the agreement, then AMC earns $10 million and SAMI earns $30 million. If both companies do not abide by the agreement, then AMC earns $15 million and SAMI earns $10 million. a. Develop a payoff matrix for this decision-making problem. b. In the absence of a binding and enforceable agreement, determine the dominantstrategy for AMC. c. Determine the dominant strategy for SAMI. d. If the two firms can enter into a binding and enforceable agreement, determine the strategy that each firm should choose.
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a) Following is payoffs matrix:-
img Above payoffs matrix shows the various outcomes of different strategies of two firms.
b) In the absence of a binding and enforceable agreement, dominant strategy for AMC is 'Not Abide'. Profit of AMC is $30 million if it both firms adopt the strategy of 'Abide'. But this is the case of prisoner dilemma where firms do not have trust in each other and they do not comply with the agreement. AMC also developed the mistrust that SAMI is most probably going to adopt the strategy of 'Not Abide'. Profit of AMC would come down to the $10 million if it goes with strategy of 'Abide and rival SAMI cheats by not abiding by the agreement.
c) Same logic can be applied in case of SAMI. SAMI dominant strategy is also 'Not to Abide'. SAMI does not have faith in AMC as the AMC is likely to cheat in this game.
d) Both firms cheat each other in the absence of any binding and enforceable agreement. Cheating by both firms leads to the lowering down of profit to down. Profit is lower when both firms not abide by the agreement. In the enforceable agreement, both firms would adopt the strategy of 'Abide' and maximize profits.

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Nike and Adidas face the following coordination problem in trying to decide whether to conduct heavy or light combative advertising against the other firm. What should each firm do Chapter 13: Best-Practice Tactics: Game Theory 483 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied img
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Following is the payoffs matrix for Nike and Adidas:
img The above payoff matrix shows different outcomes of strategies of Light Ads and Heavy Ads. The adoption of the strategy of Light ads would maximize the profits of both firms. Both firms must adopt the Light Ads or Heavy Ads. Profit is maximized at Light Ads. If one firm goes with the strategy of Heavy Ads other firms must follow the same. Varied strategies by both firms would land both in lower level of profit. Hence, Light-Light Ads or Heavy-Heavy Ads are Nash equilibrium for both firms.

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How does the analysis and the strategic equilibrium outcome differ in Exercise if the other firm enjoys a cost advantage (e.g., $35 at AA D) Then does the order of play (i.e., who goes first in making price cuts) matter in this bidding game with asymmetric costs Exercise Two insurance companies that manage employee benefit programs are bidding for additional business in their area of expertise at a market rate of $200 per hour. The potential customers refuse to leave their current suppliers and award benefit management contracts to the new firms unless billing rates are cut by $50. Abbott, Abbott Daughters (AA D) decides to do just that. Your firm, Zekiel, Zekiel Sons (ZZ S), must decide whether to match the price cut and then allow customers to choose randomly between the two firms, or whether to lower rates still further to $100 per hour. Past experience suggests, however, that the price cutting may well not stop there. The clients will surely take their best current offer back and forth between the two firms, forcing a downward price spiral. The question therefore is, "How low will you go " Crucially, this game has a stopping rule: At a price below your $40 cost, the additional business becomes unprofitable and must be refused. AA D has higher costs at $66 per hour. Again, your decision depends on an analysis of the sequence of predictable future events represented with a game tree or decision tree. Provide one. To simplify, assume that all rate cuts must be in $50 increments, that customers choose quickly between equal rate quotes using fair coin tosses (represented by capital letter N for Nature), that once a rate quote has been matched it cannot be lowered, and that many potential customers are present in the market. It is now your turn at node Z1 with rates at the $150-per-hour level. What should you do Match rates or cut rates further
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The analysis and the strategies equilibrium outcome differ in Exercise 4 if the firm AA D enjoys a cost advantage of $35 per hour. Both firms have almost same cost level and there would not be any benefit if both unnecessary involve in the competition. Hence, the both would place the bid equal to $150 per hour. It does make any difference who takes the initial step.

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INTERNATIONAL PERSPECTIVES The Superjumbo Dilemma 25 Boeing finishes assembly of wide-bodied commercial aircraft in several sizes at the rate of about one per day. Customers first pay a deposit of one-third of $84 to $127 million for a 767, one-third of $134 to $185 million for a 777, and one-third of $165 to $200 million for a 747, depending on how the planes are equipped. The second third is due after final assembly when the aircraft is painted, and the final third is due at delivery. Final assembly requires 15-25 days, the entire production schedule is 11 months long, and of course, design modifications add months to the front end of each project. The largest of the Boeing planes (the 747-400) carries 432 passengers; by comparison, the largest Airbus plane (the A380) carries 550 passengers. As early as 1993, Boeing and Airbus entered into discussions to jointly develop a very large commercial transport (VLCT) with perhaps 1,000 seats. If each firm proceeded independently, the market for VLCTs is so small relative to the massive R D costs that sizeable losses were assured. Either firm had superior profit available if it proceeded alone. Analyze this simultaneous play noncooperative product development game and predict what Boeing and Airbus would do and why. In fact, both competitors decided to enter into a strategic alliance with the option to develop a superjumbo or withdraw and maintain a wide-bodied aircraft focus. Analyze Boeing's decision in light of its $45 million contribution margin on each 747 produced and sold. Net operating profit is about $15 million. img By 2010, Airbus was projecting to deliver 93 A380s. Instead, because of delays associated with installation misdesign for the electrical harnesses, Airbus delivered only 10 planes. The cost of the delay added $6 billion to the overall development costs to be recovered. That implies the break-even production run has now risen from 250 to over 300 planes. The company has produced 45 planes each of the last two years. What about the history of Boeing's 747 production run that suggests the Airbus 380 may still be a considerable success
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Analyze the following sequential game and advise Kodak about whether they should introduce the new product, Picture CD. img
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Suppose that two Japanese companies, Hitachi and Toshiba, are the sole producers (i.e., duopolists) of a microprocessor chip used in a number of different brands of personal computers. Assume that total demand for the chips is fixed and that each firm charges the same price for the chips. Each firm's market shareand profits are a function of the magnitude of the promotional campaign used to promote its version of the chip. Also assume that only two strategies are available to each firm: a limited promotional campaign (budget) and an extensive promotional campaign (budget). If the two firms engage in a limited promotional campaign, each firm will earn a quarterly profit of $7.5 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $5.0 million. With this strategy combination, market share and total sales will be the same as for a limited promotional campaign, but promotional costs will be higher and hence profits will be lower. If either firm engages in a limited promotional campaign and the other firm undertakes an extensive promotional campaign, then the firm that adopts the extensive campaign will increase its market share and earn a profit of $9.0 million, whereas the firm that chooses the limited campaign will earn a profit of only $4.0 million. a. Develop a payoff matrix for this decision-making problem. b. In the absence of a binding and enforceable agreement, determine the dominant advertising strategy and minimum payoff for Hitachi. c. Determine the dominant advertising strategy and minimum payoff for Toshiba. d. Explain why the firms may choose not to play their dominant strategies whenever this game is repeated over multiple decision-making periods.
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Dunkin' Donuts and McDonald's McCafé have entered the specialty coffee business pioneered at Starbucks' 5,439 locations. Prices are 20 percent lower (99 cent espresso shots versus $1.45 at Starbucks), orders are simpler (Large Mocha Swirl Latte at $2.69 versus Venti Caffè Mocha at $3.35), and the wait time is under a minute versus three to five.5 Have Starbucks Frappuccinos become an affordable luxury Or are espresso coffee and flavored coffee going mainstream where Dunkin' Donuts and McDonald's have 17 percent and 15 percent of the fast-food outlet brewed coffee business, respectively, to Starbucks' 6 percent Which is happening in your city Moreover, as McCafé approaches Starbucks' market, what customer sorting rule will likely apply Is there any reason to believe Starbucks will have a different strategy in responding to Dunkin' Donuts' 4,100 stores versus the several hundred McCafés under development Why
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People who are regularly late often don't bother to carry watches. In response, other people tend to adjust to their tardiness by starting meetings 10 minutes after they're scheduled, coming to lunch appointments 10 minutes late, and so on. Analyze the following coordination game and explain why. img
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The outcomes in the bottom half of the game tree describing the last (the 20th) submarket of the chain store paradox in Figure are labeled N.A. (not applicable). Why What specific equilibrium concept in sequential games rules out the applicability of these outcomes Hint: How would you describe the game tree from node E onward as opposed to the game tree from node D onward Figure The Chain Store Paradox img
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The long competition between Subway and Quizno's subshops took price from $6 to $5 for selected Footlongs. Eventually, Quizno's dropped price another dollar to $4 with its Torpedo product. Market share rose for Quizno's relative to its head to head Footlong competition with Subway but margins suffered so much that Quizno's ingredient budgets had to be reduced substantially. Today, Subway specializes in upscale ingredients on six-inch $7 subs. Explain who came out ahead in this competition. How
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Suppose you have announced you will "meet the competition" in response to entry threats by a potential rival who has done marketing research in your target market and is offering a lower price point. What difference does it make, if any, if technology is moving very fast in the market so that this game proves to be one-time-only simultaneous play
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Why should the early adopters of an information technology system provided by IBM Systems Solutions be willing to pay more for a closed-end lease of the servers and other hardware required than for an outright purchase
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INTERNATIONAL PERSPECTIVES The Superjumbo Dilemma 25 Boeing finishes assembly of wide-bodied commercial aircraft in several sizes at the rate of about one per day. Customers first pay a deposit of one-third of $84 to $127 million for a 767, one-third of $134 to $185 million for a 777, and one-third of $165 to $200 million for a 747, depending on how the planes are equipped. The second third is due after final assembly when the aircraft is painted, and the final third is due at delivery. Final assembly requires 15-25 days, the entire production schedule is 11 months long, and of course, design modifications add months to the front end of each project. The largest of the Boeing planes (the 747-400) carries 432 passengers; by comparison, the largest Airbus plane (the A380) carries 550 passengers. As early as 1993, Boeing and Airbus entered into discussions to jointly develop a very large commercial transport (VLCT) with perhaps 1,000 seats. If each firm proceeded independently, the market for VLCTs is so small relative to the massive R D costs that sizeable losses were assured. Either firm had superior profit available if it proceeded alone. Analyze this simultaneous play noncooperative product development game and predict what Boeing and Airbus would do and why. In fact, both competitors decided to enter into a strategic alliance with the option to develop a superjumbo or withdraw and maintain a wide-bodied aircraft focus. Analyze Boeing's decision in light of its $45 million contribution margin on each 747 produced and sold. Net operating profit is about $15 million. img The European Union claims that Boeing was given $3.2 billion in tax exemptions by the State of Washington to support the Boeing Dreamliner 787 project. The United States claims that Airbus received $6 billion in loans that do not need to be repaid to support the research, development, and launch aid for the Airbus 380 Super-jumbo. These charges and countercharges at the World Trade Organization pertain to whether either firm is "dumping" the 787s and 380s brought to the export markets. These export-credit arrangements now support almost 35 percent of Airbus and Boeing sales. What category of cost must be covered by the early penetration prices in order to avoid such predatory pricing indictments
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Consider an ongoing sequence of pairwise marketing competitions between three companies with promotional campaigns of varying degrees of success. Each campaign involves comparative advertising belittling the target company. The company with the most loyal customers (call this firm "Most") enjoys 100 percent success when it attacks either of the others. The company with the least loyal customers ("Least") has a 30 percent success rate when it belittles either Most or "More." More experiences an 80 percent success rate. The firms each launch their advertising attacks one at a time in an arbitrary sequence. Least goes first and can attack either Most or More. More attacks second, and Most attacks third. If more than one of the opponents survives the first round of competition, the order of play repeats itself: Least, then More, then Most. Any player can skip his or her turn; that is, the three actions available to Least to initiate the game are as follows: attack More, attack Most, or do nothing and pass the turn. Diagram the game tree and employ subgame perfect equilibrium analysis to identify the strategic equilibrium. What should the most vulnerable firm with the least loyal customers do to initiate play What would be More's best-reply response if attacked and More survives What if Least did nothing What would Most do when and if its turn arose
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INTERNATIONAL PERSPECTIVES The Superjumbo Dilemma 25 Boeing finishes assembly of wide-bodied commercial aircraft in several sizes at the rate of about one per day. Customers first pay a deposit of one-third of $84 to $127 million for a 767, one-third of $134 to $185 million for a 777, and one-third of $165 to $200 million for a 747, depending on how the planes are equipped. The second third is due after final assembly when the aircraft is painted, and the final third is due at delivery. Final assembly requires 15-25 days, the entire production schedule is 11 months long, and of course, design modifications add months to the front end of each project. The largest of the Boeing planes (the 747-400) carries 432 passengers; by comparison, the largest Airbus plane (the A380) carries 550 passengers. As early as 1993, Boeing and Airbus entered into discussions to jointly develop a very large commercial transport (VLCT) with perhaps 1,000 seats. If each firm proceeded independently, the market for VLCTs is so small relative to the massive R D costs that sizeable losses were assured. Either firm had superior profit available if it proceeded alone. Analyze this simultaneous play noncooperative product development game and predict what Boeing and Airbus would do and why. In fact, both competitors decided to enter into a strategic alliance with the option to develop a superjumbo or withdraw and maintain a wide-bodied aircraft focus. Analyze Boeing's decision in light of its $45 million contribution margin on each 747 produced and sold. Net operating profit is about $15 million. img In 2004-2006, for the first time Boeing produced fewer planes than Airbus (see Figure). If Boeing finds itself less profitable at 60 percent market share than at 45 percent, what is the likely impact on the Airbus-Boeing tactical competition FIGURE Wide-Bodied Aircraft Deliveries by Year img
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INTERNATIONAL PERSPECTIVES The Superjumbo Dilemma 25 Boeing finishes assembly of wide-bodied commercial aircraft in several sizes at the rate of about one per day. Customers first pay a deposit of one-third of $84 to $127 million for a 767, one-third of $134 to $185 million for a 777, and one-third of $165 to $200 million for a 747, depending on how the planes are equipped. The second third is due after final assembly when the aircraft is painted, and the final third is due at delivery. Final assembly requires 15-25 days, the entire production schedule is 11 months long, and of course, design modifications add months to the front end of each project. The largest of the Boeing planes (the 747-400) carries 432 passengers; by comparison, the largest Airbus plane (the A380) carries 550 passengers. As early as 1993, Boeing and Airbus entered into discussions to jointly develop a very large commercial transport (VLCT) with perhaps 1,000 seats. If each firm proceeded independently, the market for VLCTs is so small relative to the massive R D costs that sizeable losses were assured. Either firm had superior profit available if it proceeded alone. Analyze this simultaneous play noncooperative product development game and predict what Boeing and Airbus would do and why. In fact, both competitors decided to enter into a strategic alliance with the option to develop a superjumbo or withdraw and maintain a wide-bodied aircraft focus. Analyze Boeing's decision in light of its $45 million contribution margin on each 747 produced and sold. Net operating profit is about $15 million. img In light of the foregoing payoffs, why did Airbus go ahead with the A380 Superjumbo even though its $10.7 billion development cost and rollout delays in 2010 required as many as 300 planes to break even
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Calculate the eight-hour-shift costs of operating a taxi with a medallion license that cost $125,000 borrowed at 10 percent interest assuming two shifts for 365 days per year, plus a $25,000 car that depreciates 50 percent in one year, plus $22for gas and maintenance per shift per day. Would you pay $60/shift for a taxi operator's license Why or why not
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A math graduate student explains to her friend how to approach a group of smart attractive guys who have brought along famous actor Russell Crowe. What should her friend do Ignore Russell Crowe or fixate on Russell Crowe Explain the equilibrium reasoning underlying your answer. img
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Consider the following payoff matrix: img a. Does Player A have a dominant strategy Explain why or why not. b. Does Player B have a dominant strategy Explain why or why not.
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Two insurance companies that manage employee benefit programs are bidding for additional business in their area of expertise at a market rate of $200 per hour. The potential customers refuse to leave their current suppliers and award benefit management contracts to the new firms unless billing rates are cut by $50. Abbott, Abbott Daughters (AA D) decides to do just that. Your firm, Zekiel, Zekiel Sons (ZZ S), must decide whether to match the price cut and then allow customers to choose randomly between the two firms, or whether to lower rates still further to $100 per hour. Past experience suggests, however, that the price cutting may well not stop there. The clients will surely take their best current offer back and forth between the two firms, forcing a downward price spiral. The question therefore is, "How low will you go " Crucially, this game has a stopping rule: At a price below your $40 cost, the additional business becomes unprofitable and must be refused. AA D has higher costs at $66 per hour. Again, your decision depends on an analysis of the sequence of predictable future events represented with a game tree or decision tree. Provide one. To simplify, assume that all rate cuts must be in $50 increments, that customers choose quickly between equal rate quotes using fair coin tosses (represented by capital letter N for Nature), that once a rate quote has been matched it cannot be lowered, and that many potential customers are present in the market. It is now your turn at node Z1 with rates at the $150-per-hour level. What should you do Match rates or cut rates further
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