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Class7 Game Theory in Decisions.pdf - Managerial Economics...

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Managerial EconomicsPart VII. Game Theory in Decision Making1.In a two-player, one-shot, simultaneous-move game, each player can choose strategyAstrategyB.If both players choose strategyA,each earns a payoff of $400. If both playerschoose strategyB,each earns a payoff of $200. If player 1 chooses strategyAand player 2chooses strategyB,then player 1 earns $100 and player 2 earns $600. If player 1 choosesstrategyBand player 2 chooses strategyA,then player 1 earns $600 and player 2 earns $100.a)Write the above game in normal form.b)Find each player’s dominant strategy, if it exists.c)Find the Nash equilibrium (or equilibria) of this game.2.In mid-2010, Saudi Arabia and Venezuela (both members of OPEC) produced an average of8 million and 3 million barrels of oil a day, respectively. Production costs were about $20 perbarrel, and the price of oil averaged $80 per barrel. Each country had the capacity to producean extra 1 million barrels per day. At that time, it was estimated that each 1-million-barrelincrease in supply would depress the average price of oil by $10. What actions should eachcountry take and why?3.Suppose that US-based Qualcomm and European-based T-Mobile are contemplatinginfrastructure investments in a developing mobile telephone market. Qualcomm currently usesa code-division multiple access (CDMA) technology, which almost 67 million users in theUnited States utilize. In contrast, T-Mobile uses a global system for mobile communication(GSM) technology that has become the standard in Europe and Asia. Each company must(simultaneously and independently) decide which of these two technologies to introduce inthe new market. Qualcomm estimates that it will cost $1.2 billion to install its CDMAtechnology and $2.0 billion to install GSM technology T-Mobile’s projected cost of installingGSM technology is $1.1 billion, while the cost of installing the CDMA technology is $2.7billion. As shown in the accompanying table, each company’s projected profits (in billions)depend not only on the technology it adopts, but also on that adopted by its rival. Constructthe normal form of this game. Then, explain the economic forces that give rise to the structureof the payoffs and any difficulties the companies might have in achieving Nash equilibriumin the new market.Standards(Qualcomm - T-Mobile)Qualcomm’sProfitsT-Mobile’sprofitsCDMA-GSM$13.5$9.7CDMA-CDMA$17.2$15.6GSM-CDMA$16.7$10.1GSM-GSM$15.5$19.84.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 personalcomputers. Assume that total demand for the chips is fixed and that each firm charges thesame price for the chips. Each firm’s market share and profits are a function of the magnitudeof the promotional campaign used to promote its version of the chip. Also assume that onlytwo strategies are available to each firm: a limited promotional campaign and an extensivepromotional campaign. If the two firms engage in a limited promotional campaign, each firmwill earn a quarterly profit of $7.5 million. If the two firms undertake an extensive promotionalcampaign, each firm will earn a quarterly profit of $5 million. With this strategy combination,market share and total sales will be the same as for a limited promotional campaign, butor
Managerial Economicspromotional costs will be higher and hence profits will be lower. If either firm engages in alimited promotional campaign and the other firm undertakes an extensive promotionalcampaign, then the firm that adopts the extensive campaign will increase its market share andearn a profit of $9.0 million, whereas the firm that chooses the limited campaign will earn aprofit of only $4 million.a)Develop a payoff matrix for this decision-making problem.b)In the absence of a binding and enforceable agreement, determine the dominantadvertising 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 thisgame is repeated over multiple decision-making periods.5.Firms J and K produce video game consoles and compete against one another. Each firm candevelop either an economy console (E) or a deluxe model (D). According to the bestavailable marketresearch, the firms’ resulting profits are given by the accompanyingpayofftable. The firms make their decision independently, and each is seeking its own maximumprofit. Is it possible to make a confident prediction concerning their actions and theoutcome?Firm KED

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Term
Winter
Professor
business
Tags
Game Theory, Auction, Soft drink, Qualcomm

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