Exam 13: Game Theory and Competitive Strategy

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If, in the game in Scenario 13.14, R moves first, C will respond with

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Scenario 13.9 Consider the following game: Two firms are situated next to a lake, and it costs each firm $1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is $1,000 times the number of polluting firms. Scenario 13.9 Consider the following game: Two firms are situated next to a lake, and it costs each firm $1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is $1,000 times the number of polluting firms.   -Refer to Scenario 13.9. What kind of game is being played by Lago and Nessie? -Refer to Scenario 13.9. What kind of game is being played by Lago and Nessie?

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Scenario 13.3 Consider the following game: Scenario 13.3 Consider the following game:   -Which of the following is true for the game in Scenario 13.3? -Which of the following is true for the game in Scenario 13.3?

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In the sequential version of a game using the same players, the same strategies, and the same possible outcomes as the original game, the equilibrium:

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A strategy A is "dominant" for a player X if:

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When cost and demand are stable over time in an industry, repetition of Prisoners' Dilemma situations:

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Consider two firms, X and Y, that produce super computers. Each can produce the next generation super computer for the military (M) or for civilian research (C). However, only one can successfully produce for both markets simultaneously. Also, if one produces M, the other might not be able to successfully produce M, because of the limited market. The following payoff matrix illustrates the problem. Consider two firms, X and Y, that produce super computers. Each can produce the next generation super computer for the military (M) or for civilian research (C). However, only one can successfully produce for both markets simultaneously. Also, if one produces M, the other might not be able to successfully produce M, because of the limited market. The following payoff matrix illustrates the problem.   a. Find the Nash equilibrium, and explain why it is a Nash equilibrium. b. If Firm X were unsure that the management of Firm Y were rational, what would Firm X choose to do if it followed a maximin strategy? What would both firms do if they both followed a maximin strategy? a. Find the Nash equilibrium, and explain why it is a Nash equilibrium. b. If Firm X were unsure that the management of Firm Y were rational, what would Firm X choose to do if it followed a maximin strategy? What would both firms do if they both followed a maximin strategy?

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Scenario 13.13 Consider the game below: Scenario 13.13 Consider the game below:   -If the game in Scenario 13.13 were not played sequentially, -If the game in Scenario 13.13 were not played sequentially,

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As defined by Thomas Schelling, a "strategic move" is:

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Joe's Imports is currently the only dealer for imported Sporto autos on the East Coast, but Fred's Autos may enter the import market and start selling Sporto cars in the East Coast market during the coming year. Joe's Imports can pay the Sporto manufacturer for exclusive East Coast marketing rights, which would deter the entry of Fred's Autos into the market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes of the sequential entry game are summarized in the following matrix: Joe's Imports is currently the only dealer for imported Sporto autos on the East Coast, but Fred's Autos may enter the import market and start selling Sporto cars in the East Coast market during the coming year. Joe's Imports can pay the Sporto manufacturer for exclusive East Coast marketing rights, which would deter the entry of Fred's Autos into the market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes of the sequential entry game are summarized in the following matrix:   What is the equilibrium outcome from this sequential entry game? What is the equilibrium outcome from this sequential entry game?

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Joanna has a credit card account with Card Bank. Card Bank's available strategies are to raise Joanna's credit card interest rate or do nothing. Joanna's available strategies are to transfer her Card Bank account balance to another creditor or do nothing. The strategy payoffs are indicated below. Joanna has a credit card account with Card Bank. Card Bank's available strategies are to raise Joanna's credit card interest rate or do nothing. Joanna's available strategies are to transfer her Card Bank account balance to another creditor or do nothing. The strategy payoffs are indicated below.   Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game? Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game?

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Scenario 13.6 Consider the following game. Payoffs are in millions of dollars. Scenario 13.6 Consider the following game. Payoffs are in millions of dollars.   -In the game in Scenario 13.6, what is the Nash equilibrium? -In the game in Scenario 13.6, what is the Nash equilibrium?

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Gym X and Bodyworks are both going to open an exercise facility in the local market. Each company may decide to open a facility concentrating on cardio equipment for customers interested in mostly aerobic workouts. Another alternative for each company is to open a facility concentrating on muscle building equipment for customers interested mostly in bodybuilding workouts. The payoff matrix for each company dependent upon their strategies and that of their competitor is given below. Gym X and Bodyworks are both going to open an exercise facility in the local market. Each company may decide to open a facility concentrating on cardio equipment for customers interested in mostly aerobic workouts. Another alternative for each company is to open a facility concentrating on muscle building equipment for customers interested mostly in bodybuilding workouts. The payoff matrix for each company dependent upon their strategies and that of their competitor is given below.   Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game? Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game?

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The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma. The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma.   a. Does either firm have a dominant strategy? What strategy should each firm follow? b. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy. c. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational? a. Does either firm have a dominant strategy? What strategy should each firm follow? b. Assume that the game is to be played an infinite number of times. (Or, equivalently, imagine that neither firm knows for certain when rounds of the game will end, so there is always a positive chance that another round is to be played after the present one.) Would the tit-for-tat strategy would be a reasonable choice? Explain this strategy. c. Assume that the game is to be played a very large (but finite) number of times. What is the appropriate strategy if both firms are always rational?

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It can be rational to play tit-for-tat in a repeated Prisoners' Dilemma game:

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Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs:   What are the dominant strategies in this game? What are the dominant strategies in this game?

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Tony and Larry are managers of baseball teams that currently playing a game. It's late in the ballgame and Tony's team is currently winning and in the field. Tony's strategies are to bring in a right handed pitcher (RHP) or to bring in a left handed pitcher (LHP). Larry's strategies are to bring in a right handed pinch hitter (RPH) or to bring in a left handed pinch hitter (LPH). The payoff matrix is in terms of winning (W) or losing (L) the game. Does either player have a dominant strategy? Does the game have a Nash equilibrium? What is the maximin strategy of each player in the game? Tony and Larry are managers of baseball teams that currently playing a game. It's late in the ballgame and Tony's team is currently winning and in the field. Tony's strategies are to bring in a right handed pitcher (RHP) or to bring in a left handed pitcher (LHP). Larry's strategies are to bring in a right handed pinch hitter (RPH) or to bring in a left handed pinch hitter (LPH). The payoff matrix is in terms of winning (W) or losing (L) the game. Does either player have a dominant strategy? Does the game have a Nash equilibrium? What is the maximin strategy of each player in the game?

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Use the following statements to answer this question: I. If mixed strategies are allowed, every game has at least one Nash equilibrium. II) The maximin strategy is optimal in the game of "matching pennies."

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Scenario 13.17 Consider the entry-deterrence game below. The potential entrant would have to spend some amount in sunk costs to enter the market. Scenario 13.17 Consider the entry-deterrence game below. The potential entrant would have to spend some amount in sunk costs to enter the market.   -In the game in Scenario 13.17, Incumbent Monopoly has: -In the game in Scenario 13.17, Incumbent Monopoly has:

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If Simple were able to move first in a sequential version of the game in Scenario 13.15, the equilibrium would be:

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