Exam 12: Game Theory

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(Table: Hitter and Pitcher I) (Table: Hitter and Pitcher I)    a. What is the hitter's dominant strategy? b. What is the pitcher's dominant strategy? c. What is the pure-strategy Nash equilibrium? d. What is the mixed-strategy Nash equilibrium? a. What is the hitter's dominant strategy? b. What is the pitcher's dominant strategy? c. What is the pure-strategy Nash equilibrium? d. What is the mixed-strategy Nash equilibrium?

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Imagine two friends, Marcus and Marty, who are providing goods for a bake sale. They can take either brownies or cookies, and payoffs (the profits that they will split) are as given in the table: Imagine two friends, Marcus and Marty, who are providing goods for a bake sale. They can take either brownies or cookies, and payoffs (the profits that they will split) are as given in the table:   There is a pure-strategy Nash equilibrium at ____ There is a pure-strategy Nash equilibrium at ____

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(Table: Hitter and Pitcher I) (Table: Hitter and Pitcher I)   The pitcher's dominant strategy is ____. The pitcher's dominant strategy is ____.

(Multiple Choice)
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Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table.   There exists a mixed-strategy Nash equilibrium when Kohar chooses Apartment 1 with probability ____. There exists a mixed-strategy Nash equilibrium when Kohar chooses Apartment 1 with probability ____.

(Multiple Choice)
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(Table: Jack and Jill I) (Table: Jack and Jill I)    a. What are Jack's strategies? b. What are Jill's strategies? c. If Jack chooses to climb the hill and Jill doesn't bring the pail, what are the payoffs to Jack and Jill? d. If Jack chooses to not climb the hill and Jill brings the pail, what are the payoffs to Jack and Jill? a. What are Jack's strategies? b. What are Jill's strategies? c. If Jack chooses to climb the hill and Jill doesn't bring the pail, what are the payoffs to Jack and Jill? d. If Jack chooses to not climb the hill and Jill brings the pail, what are the payoffs to Jack and Jill?

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(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. (Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood.   Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.2, then the players ____. Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.2, then the players ____.

(Multiple Choice)
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(Figure: Firms A and B VII) (Figure: Firms A and B VII)   Which of the panels correctly illustrates trimming the branches? Which of the panels correctly illustrates trimming the branches?

(Multiple Choice)
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(Figure: Players A and B V) (Figure: Players A and B V)   Suppose that Player A promises a $2 side payment to Player B if Player B chooses pass. As a result of the side payment, the game's outcome will change from: Suppose that Player A promises a $2 side payment to Player B if Player B chooses pass. As a result of the side payment, the game's outcome will change from:

(Multiple Choice)
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(Table: Helicopter Rides I) Payoffs are profits in thousands of dollars. (Table: Helicopter Rides I) Payoffs are profits in thousands of dollars.   Which of the following statements is TRUE? Which of the following statements is TRUE?

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(Table: Simultaneous Game I) Raina and Trina are playing a simultaneous game. (Table: Simultaneous Game I) Raina and Trina are playing a simultaneous game.   Raina's dominant strategy is _____, and Trina's dominant strategy is _____. Raina's dominant strategy is _____, and Trina's dominant strategy is _____.

(Multiple Choice)
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(Table: Firms A and B XI) Represent the normal-form game as a sequential game, with Firm A making the first decision. What is the outcome of this game? (Table: Firms A and B XI) Represent the normal-form game as a sequential game, with Firm A making the first decision. What is the outcome of this game?

(Essay)
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Suppose that Fizzy Soda and Townie Soda must choose whether to advertise their soft drinks. In a Nash equilibrium, both firms choose to advertise and earn weekly profits of $80,000. Which of the following statements is (are) TRUE? I. Neither firm has incentive to change its advertising strategy, given the strategy choice of its rival. II. If Townie Soda decided to stop advertising, its profits would fall below $80,000. III. If both firms stopped advertising, it is possible that each firm could earn profits greater than $80,000.

(Multiple Choice)
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(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. (Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following.   The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game. The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game.

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Nancy and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together and they might go apart. Their payoffs in terms of their happiness are as follows. Nancy and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together and they might go apart. Their payoffs in terms of their happiness are as follows.    a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium? a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

(Essay)
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The following game: The following game:

(Multiple Choice)
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Imagine two friends, Marcus and Marty, who are providing goods for a bake sale. They can take either brownies or cookies, and payoffs (the profits that they will split) are as given in the table: Imagine two friends, Marcus and Marty, who are providing goods for a bake sale. They can take either brownies or cookies, and payoffs (the profits that they will split) are as given in the table:    a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium? a. What are the pure-strategy Nash equilibria if any? b. What is the mixed-strategy Nash equilibrium?

(Essay)
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Answer the following questions. a. What is backward induction? b. What is a grim trigger strategy? c. What is a tit-for-tat strategy?

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(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. (Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following.   The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game. The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game.

(Multiple Choice)
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(Table: Hitter and Pitcher I) (Table: Hitter and Pitcher I)   A pure-strategy Nash Equilibrium in this game is ____. A pure-strategy Nash Equilibrium in this game is ____.

(Multiple Choice)
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(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. (Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following.   The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game. The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game.

(Multiple Choice)
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