Exam 12: Game Theory

(Table: Firms 1 and 2 III) Payoffs represent profits in millions of dollars. Firm 1's dominated strategy is ____.

(Figure: China and United States I) a. What is the Nash equilibrium of this game? b. Is it credible for the United States to threaten to blow up the world if China invades Taiwan?

A simultaneous game:

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player A chooses Up with probability ____.

Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. There is a pure-strategy Nash equilibrium at ____.

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 Karoun chooses Apartment 1 with probability ____.

(Table: Firms 1 and 2 III) Payoffs represent profits in millions of dollars. Firm 2's dominated strategy is ____.

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There is a pure-strategy Nash equilibrium at ____.

(Figure: Firms A and B IV) Two firms are considering whether to expand their production capacity. Which of the following statements is TRUE?

(Table: Firms A and B XIII) In a simultaneous game, the Nash equilibrium is Firm A choosing ____ and Firm B choosing ____.

(Table: Firms A and B IX) Two firms have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period. Both firms are using a grim trigger strategy. The value of d (discount rate) = ____ would make Firm A indifferent between keeping the agreement or cheating on the agreement.

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player B chooses Left with probability ____.

Lala and Marmar are deciding whether to reserve a vacation room with a city view or an ocean view. 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?

(Table: Players A and B IV) Payoffs represent profits in millions of dollars. Which of the following statements is (are) TRUE? I. In a simultaneous game that is played only once, the Nash equilibrium is (0 , 0). II. In a sequential game in which Player A moves first, the Nash equilibrium is (6 , 0). III. In the sequential game, Player A has a first-mover advantage.

(Figure: Darya and Anya I) a. What is the Nash equilibrium of this game? b. Explain how Darya could use a side payment to make herself better off. What is the size of the side payment?

(Table: Players A and B VIII) In Table 2, ____ is a Nash Equilibrium.

(Table: Players 1 and 2 II) The payoffs represent dollars. If both players follow their maximin strategy, the outcome of this game is:

(Table: Jack and Jill I) If Jack chooses to climb the hill and Jill does not bring the pail, Jill's payoff is ____.

(Table: Owens Corning and GAF Capacity Expansion I) Payoffs represent profits in millions of dollars. The Nash equilibrium:

(Table: Hanes and Fruit of the Loom T-Shirts I) Payoffs represent profits in thousands of dollars. What is the Nash equilibrium?