Exam 12: Game Theory

The lesson from Dr. Strangelove is that:

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 2 with probability ____.

The following game has _____ pure-strategy equilibrium (equilibria) and (but) _____ mixed-strategy equilibrium (equilibria).

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 exists a mixed-strategy Nash equilibrium when Dennis chooses hiking with a probability of ____.

Bob and Rosalie are deciding whether to request fish or chicken at a wedding that they will attend. If they order different meals, they can try each of the dishes by sharing. 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: Owens Corning and GAF Capacity Expansion I) Payoffs represent profits in millions of dollars. What is Owens Corning's dominated strategy?

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 ____

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

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

(Table: Fresh Fruit Market and Spoiled Not Food I) Payoffs are in thousands of dollars. Fresh Fruit Market's dominant strategy is ____.

(Table: Players A and B III) The payoffs represent profits in thousands of dollars. Which of the following statements is (are) TRUE? I. In a simultaneous game that is played only once, the Nash equilibrium is (20 , 20). II. In a sequential game in which Player A moves first, the Nash equilibrium is (18 , 18). III. In the sequential game, Player A has a first-mover advantage.

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

To solve for a mixed-strategy equilibrium in a two-player, two-strategy game (two-by-two game):

(Table: Fresh Fruit Market and Spoiled Not Food I) Payoffs are in thousands of dollars. Spoiled Not Food's dominant strategy is ____.

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

Consider the following game. Find all pure-strategy Nash equilibria.

(Table: Simultaneous Game II) Tatyana and Lena have been arrested for a crime. In this simultaneous game, the payoffs represent years in jail. It should be noted that years in jail are something that someone would like to avoid or are considered negatively. Lena's dominated strategy is ______, while Tatyana's dominated strategy is _________.

The following game:

(Table: Firms 1 and 2 III) Payoffs represent profits in millions of dollars. a. What is Firm 2's dominant strategy? b. What is Firm 2's dominated strategy? c. At what values of x will Firm 1's dominant strategy be down? d. If x = 7, what is Firm 1's dominated strategy?

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 exists a mixed-strategy Nash equilibrium when Denise chooses hiking with a probability of ____.